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# Recent problems solved by 'oberobic'

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 Length-and-distance/283748: A square has vertices U(-2,1), V(2,3), W(4,-1) and X(0,-3). Verify that the diagonals perpendicularly bisect each other.1 solutions Answer 205929 by oberobic(2304)   on 2010-03-21 22:41:02 (Show Source): You can put this solution on YOUR website!The four points can be plotted: . . The diagonals are defined by the points: U,W and V,X. . We need to solve for a line going through the first pair of points U (-2,1) W (4,-1) . y = mx + b m= (-1-1)/(4-(-2))= -2/6 = -1/3 y = -1/3x + b We can solve for 'b' by plugging in the points we know. 1 = -1/3*(-2 ) + b b = 1/3 or -1 = -1/3*4 +b b = 1/3 . y=-1/3x + 1/3 defines the equation for the first diagonal. . Then we need to find the equation for the line going through the other two points V (2,3) X (0,-3) m= (-3-3)/(0-2) = -6/-2 = 6/2 = 3 . At this point we know the diagonals are perpendicular because, by definition, the slopes of perpendicular lines are the negative reciprocal. -1/3 is the negative reciprocal of 3. . But we can press on to continue to define the second equation... . -3 = 3(0) + b b = -3 or 3 = 3(2) + b b = -3 y = 3x -3 . Then a graph will illustrate they are perpendicular. .
 Mixture_Word_Problems/283738: please help with this problem a 10% acid solution is to be mixed with a 50% acid solution in order to get 120 ml of a 20% acid solution. how many ml of the 10% solution and 50% should be mixed?1 solutions Answer 205920 by oberobic(2304)   on 2010-03-21 22:03:03 (Show Source): You can put this solution on YOUR website!With solution problems, you need to keep track of the amount of 'pure' stuff. You need to end up with 120 ml of a 20% solution, so that is .20 * 120 = 24 ml of 'pure' acid 120-24 = 96 ml of water . x = volume of 10% acid y = volume of 50% acid . x+y = 120 ml . It is better to set up the equation with the minimum number of unknowns. In this case, we know the 120 ml is required, so we can say: x = volume of 10% acid 120-x = volume of 50% acid . .1*x + .5(120-x) = .2*120 . multiply both sides of the equation by 10 to get rid of decimals . 10*(.1*x + .5(120-x)) = 10*(.2*120) 10*(.1*x) + 10(.5(120-x)) = 10*(.2*120) x + 5(120-x) = 2*120 . x + 600 -5x = 240 . -4x = -360 . x = 90 . y = 120-90 = 30 . Checking, how much 'pure' stuff we would have... .1*90 = 9 ml .5*30 = 15 ml 9+15 = 24 ml, which is what we needed . So the answer is: 90 ml of a 10% solution plus 30 ml of a 50% solution to produce 120 ml of 20% solution. . Done
 Geometry_Word_Problems/283707: the diagonal of a square is 62 feet. What is the perimeter?1 solutions Answer 205916 by oberobic(2304)   on 2010-03-21 21:49:31 (Show Source): You can put this solution on YOUR website!The diagonal of a square is the hypotenuse of a triangle. . c^2 = a^2 + b^2 . Since it is a square, a=b. . 62^2 = a^2 + b^2 = a^2 + a^2 . 62^2 = 2a^2 . 3844 = 2a^2 . 2a^2 = 3844 . a^2 = 1922 . a = sqrt(1922) . a = 43.84 . So, the perimeter = 4*43.84 = 175.35 or about 176 . Done
 expressions/283731: does -2 solve the equation -5-3=1? 1 solutions Answer 205910 by oberobic(2304)   on 2010-03-21 21:38:45 (Show Source): You can put this solution on YOUR website!No. -5-3=-8.
 Numeric_Fractions/283723: What is 29.6% written as a fraction?1 solutions Answer 205907 by oberobic(2304)   on 2010-03-21 21:30:50 (Show Source): You can put this solution on YOUR website!Any number that can be written as a fraction is, by definition, a rational number. . 29.6% is mathematically = 0.296. . And we see that .296 = 296 thousandths, which we can show as: . . . The 8's cancel, so we end up with . . Done.
 Miscellaneous_Word_Problems/283717: Lydia, Sarah, and Denise collected campain buttons. Lydia had 20 more buttons than Sarah. Denise had 3 times as many buttons as Sarah. If the total number of campaign buttons the 3 girls had was 120, how many buttons did Lydia have?1 solutions Answer 205901 by oberobic(2304)   on 2010-03-21 21:21:25 (Show Source): You can put this solution on YOUR website!L = number of buttons collected by Lydia S = number of buttons collected by Sarah D = number of buttons collected by Denise L + S + D = 120 :: Total given. . L = S + 20 :: Lydia has 20 more than Sarah D = 3S :: Denise had 3 times as many as Sarah . Question: How many did Lydia have? . We have 3 unknowns, so we need 3 equations... OR We need to redefine the variables to use fewer than 3 unknowns. . Looking back, the problem was stated in terms of Sarah's buttons. . L = S+20 D = 3S and S = S of course . L + D + S = 120 :: given . substituting... . (S+20) + 3S + S = 120 5S = 100 S = 20 . Substituting this value . L = S + 20 L = 20 + 20 = 40 . D = 3S D = 3(20) = 60 . Checking, does L+S+D = 120? 20 + 40 +60 = 120 Yes! . Rechecking the question, it only asks how many Lydia has. . Answer: Lydia has 40 buttons. . Done.
 Square-cubic-other-roots/283671: I need to solve using Completing the square x squared=-4x-21 solutions Answer 205856 by oberobic(2304)   on 2010-03-21 20:03:36 (Show Source): You can put this solution on YOUR website! . Add 4x to both sides . . This is conceptually ax^2 + bx = c . To complete the square, take 1/2*b, square it, and add it as a new 'c'. . . . . . . hmmmm....that means we have an imaginary number in here, since we have a squared term on the left and a negative number on the right. . .
 Complex_Numbers/283669: (4+5i)(2-3i)1 solutions Answer 205852 by oberobic(2304)   on 2010-03-21 19:54:43 (Show Source):
 Polynomials-and-rational-expressions/283663: In a triangle one angle is 23 degrees more than the smallest angle the third angle is 10 degrees more than the sum of the other two angles find the measurement of each angle I can not figure out how to write this problem out my book has nothing like it and I cant find it online PLEASE HELP1 solutions Answer 205850 by oberobic(2304)   on 2010-03-21 19:51:04 (Show Source): You can put this solution on YOUR website!The triangle has 3 angles: a, b, and c. We know that a + b + c = 180 degrees because all triangles have 180 degrees. . We'll pick 'a' as the smallest angle. . b = a + 23 :: given . c = a+b+10 :: given . So, it seems we have 3 unknowns and not enough equations to solve them. . But let's think about it. . We have a = a . b = a+23 . c = a+b+10 . for 'c', substitute b=a+23 . c = a + (a+23) +10 . a + b + c = 180, so... a + (a+23) + (a+(a+23)+10) = 180 . 4a + 56 = 180 4a = 124 a = 31 . b = a +23 b = 31+23 = 54 . c = a + b + 10 c = 31 + 54 + 10 = 95 . Do they add up to 180? 31 + 54 + 95 = 180 Correct. . The three angles are: 31, 54, and 95. . Done.
 Square-cubic-other-roots/283662: I don't understand why 2/3 can become 2 times 1/3. Can you shed light on this? 1 solutions Answer 205848 by oberobic(2304)   on 2010-03-21 19:42:12 (Show Source): You can put this solution on YOUR website! . This is a basic concept you need to take the time to understand. . Consider 3/4... . Or 1/2... . Etc.
 Coordinate-system/283656: a) Solve by graphing: y = x + 4 y = -2x + 1 b) Tell what you can about the solution. 1 solutions Answer 205845 by oberobic(2304)   on 2010-03-21 19:35:24 (Show Source): You can put this solution on YOUR website!y = x +4 is shown in red. y = -2x+1 is shown in green. Graphing... . . The point of intersection is (-1,3), which is the single solution. Since there is at least one solution, we can say the equations are consistent. The y-intercept of y=x+4 is (0,4) The x-intercept of y=x+4 is (-4,0) The slope of y=x+4 = 1, so the line slopes up to the right. The y-intercept of y=-2x+1 is (0,1). The x=intercept of y=-2x+1 is (1/2,0). The slope of y=-2x+1 is -2, so the line slopes down to the right. . Done.
Graphs/283642: The length of a rectangle is 3cm more than 2 times its width. If the area of the rectangle is 93cm^2, find the dimensions of the rectangle. Enter your answers in the blanks. Enter only the numeric values rounded to the nearest thousandth of centimeter Width=________cm, Length=_____________cm.
1 solutions

Answer 205843 by oberobic(2304)   on 2010-03-21 19:24:48 (Show Source):
You can put this solution on YOUR website!
L = length
W = width
A = area
A = L*W
.
L = 2W + 3
.
A = 93 cm^2
.
Substitute L = 2W+3 in the area equation to solve.
.
L*W = 93 cm^2
(2W +3) * W = 93
2W^2 + 3W = 93
2W^2 + 3W -93 = 0
.
This does not factor nicely, so you need to use the quadratic equation.
.
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=753 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6.11021136700612, -7.61021136700612. Here's your graph:

.
This provides two solutions: W=6.11 and W=-7.61.
W cannot be negative, so the approximate value is W=6.11.
.
Substituting, W=6.11, we can find L.
L = 93/6.11
L = 15.22 cm
.
Checking, does the area = 93 cm^2?
(15.22)(6.11) = 92.9942 cm^2, which is close enough to 93.
Correct.
.
Checking, does L = 2W + 3?
2W = 2*6.11 = 12.22 cm
12.22 + 3 = 15.22 cm
Correct.
.
L = 15.22 cm
W = 6.11 cm
.
Done.

 Angles/283601: Can you please help me understand and solve this problem: One angle is 15 degrees less than twice another angle. If the angles are complementary find each angle1 solutions Answer 205830 by oberobic(2304)   on 2010-03-21 18:19:27 (Show Source): You can put this solution on YOUR website!If angles are complementary, then the sum to 90 degrees. We have two angles, say 'x' and 'y'. We know from the problem statement they are complementary, so x+y=90 Given this equation, we can see that it is easier to define them as: 'x' and '90-x'. . That leaves us with only one unknown to solve. . In algebra, we'd say: x = x y = 90-x . We also are told one angle is 15 less than twice the other. So if we add 15 to one of the angles, it will equal twice the other angle. . y+15 = 2x . Which means y = 2x - 15 . Returning to the objective equation: . x + y = 90 . Substitute y = 2x-15 . x + 2x-15 = 90 3x -15 = 90 3x = 105 x = 35 . x + y = 90 y = 90 -35 y = 55 . Check to see if these values satisfy the other problem statement: y + 15 = 2x y+15 = 55+15 = 70 2x = 2*35 = 70 Correct. . Answer: The two angles are: 35 and 55. . Done.
 Travel_Word_Problems/283591: The length of the minute hand on the clock is 7 inches. What is the most reasonable measure of the distance that the tip of the minute hand travels in one hour? 1 solutions Answer 205825 by oberobic(2304)   on 2010-03-21 18:08:16 (Show Source): You can put this solution on YOUR website!The minute hand describes a circle as it sweeps across the traditional analog clock face. The radius of the circle is 7 inches. The circumference of the circle is the pi*diameter. The diameter = 2*radius. C = 2*7*pi C = 43.98222972 inches . I cannot say what your teacher would consider "the most reasonable measure." Perhaps 44 inches is "the most reasonable measure?" . Done.
 Linear-systems/283595: graphing lines in standard form 4x-y=31 solutions Answer 205821 by oberobic(2304)   on 2010-03-21 18:03:51 (Show Source): You can put this solution on YOUR website!A linear equation in standard form is: Ax + By = C . We have: 4x -y = 3 . That is already in standard form. . To graph a line, you need two points. . I usually pick the y-intercept and x-intercept. The y-intercept is where x=0. The x-intercept is where y=0. . y-intercept: 4(0) -y = 3 -y = 3 y = -3 (0,-3) . x=intercept: 4x -0 = 3 4x = 3 x = 3/4 (3/4,0) . Now you can graph it. .
 Quadratic_Equations/283583: Marvin wants to purchase a rectangular rug. it has an area of 80 square ft. he cannot remember the length and width, but he remembers that the length was 8 more than some number and the width was 8 more than the same number. What is the quadratic eqation that can be made from the above information?1 solutions Answer 205815 by oberobic(2304)   on 2010-03-21 17:58:03 (Show Source): You can put this solution on YOUR website!Let 'some number' be 'x'. L = length = x + 8 W = width = x + 8 . The transitive property teaches that if a=b and b=c, then a=c. Therefore, L = W. That means the rug is square. Of course, a square is an equilateral rectangle, so that is okay. . A = area = L*W = L^2 = W^2 = 80 sq. ft. . L = sqrt(80) = sqrt(16*5) = sqrt(16)*sqrt(5) = 4*sqrt(5) = 8.94427191 . So L = W = 8.94427191 . Returning to the setup, L = x+8 = 8 + .94427191. So x = .94427191 No wonder he could not remember it. . Done.
 Exponents/283561: Rewrite the following expression with positive exponents Choose the correct equivalent expression. A) B) C) D) 1 solutions Answer 205804 by oberobic(2304)   on 2010-03-21 17:44:09 (Show Source):
 Graphs/283485: find the equation of the line that passes through (4,-3) and (8,-5)1 solutions Answer 205759 by oberobic(2304)   on 2010-03-21 15:02:52 (Show Source): You can put this solution on YOUR website!We are seeking an equation for a line that will go through the points (4,-3) and (8,-5). . We know the slope-intercept form of the equation is: y = mx+b m = slope b = y-intercept . m = rise / run = change in y / change in x . m = (y2-y1)/(x2-x1) . (4,-3) = (x1,y1) (8,-5) = (x2,y2) . m = (-5 -(-3)) / (8 -4) = (-5 +3) / (8 -4) = -2/4 = -1/2 . y = -1/2x + b . Now we can substitute what we know to find 'b'. For example, one of the points is (4,-3). Substituting for x and y... . -3 = -1/2(4) + b -3 = -2 + b -1 = b . And we know the other point is (8,-5) . -5 = -1/2(8) + b -5 = -4 + b -1 = b . b = -1 = y-intercept = (0,-1) . y = -1/2x -1 . Another useful point to find is the x-intercept, which is where y=0. . 0 = -1/2x -1 1/2x = -1 x = -2 (-2,0) . Graph to check . . Answer: The equation is . Done
 Numeric_Fractions/283486: My question is what is the answer to 9/16 +9/16 ?1 solutions Answer 205756 by oberobic(2304)   on 2010-03-21 14:48:43 (Show Source): You can put this solution on YOUR website!Since they have the same denominator, we know that: . We notice that 18 > 16, so we can reverse the idea to say: . . Of course, 2/16 can be further simplified by dividing by 2: . . Done
 Polynomials-and-rational-expressions/283475: Two times the reciprocal of an integer, plus 4 times the reciprocal of 3 times the integer is 1/3. find the integer.1 solutions Answer 205755 by oberobic(2304)   on 2010-03-21 14:45:31 (Show Source): You can put this solution on YOUR website!The reciprocal of x is 1/x. . . '3x' is the common denominator, so multiply through by 3x to cancel the denominators. . . Checking... . . Correct . The integer is x=10. . Done
 Quadratic_Equations/283479: Solve the equation by graphing x to the second - 8x + 7 = 0 (answer has to be a curved line)1 solutions Answer 205753 by oberobic(2304)   on 2010-03-21 14:36:22 (Show Source): You can put this solution on YOUR website!x^2 -8x + 7 = 0 is a quadratic equation. . We can factor it. . (x-1)(x-7) = 0 . So x = 1 or x = 7, which are the points (1,0) and (7,0). . .
 Linear-equations/283476: graph the equation and identify the Y intercetpt Y=3x-91 solutions Answer 205752 by oberobic(2304)   on 2010-03-21 14:33:28 (Show Source): You can put this solution on YOUR website!The given formula is in slope-intercept form: y = mx + b. y = 3x -9 . The y-intercept is the point where x=0, so we see it is 'b', which equals -9, or the point (0,-9). The x-intercept is the point where y=0, so we see it is x=3, or the point (3,0). With two points you can draw a straight line. .
 Sequences-and-series/283474: Find two numbers whose sum is 55 and product is 600.1 solutions Answer 205750 by oberobic(2304)   on 2010-03-21 14:30:15 (Show Source): You can put this solution on YOUR website!"Two numbers" suggests we use 'x' and 'y'. However, we are told they sum to 55: x + y = 55 That means we can substitute 55-x for y. That, in turn, means we have only one unknown to solve. . We also are told that x*y = 600 Substituting y = 55-x . x*(55-x) = 600 55x -x^2 = 600 . Add x^2 to both sides 55x = x^2 + 600 . Subtract 55x from both sides 0 = x^2 -55x + 600 . Factor . (x-15)(x-40)=0 . So we we have two possible values for x: 15 and 40. That means we have two possible values for y: 55-15 = 40 and 55-40 = 15. . Answer: The two numbers are 15 and 40. Their sum is 55. Their product is 600. . Done.
 Polynomials-and-rational-expressions/283303: two cars leave an intersection, one car travels north the other east. When the car traveling north had gone 12 miles the distance between the cars was 8 miles more than the distance traveled by the car heading east. how far had the eastbound car traveled?1 solutions Answer 205653 by oberobic(2304)   on 2010-03-20 22:32:05 (Show Source): You can put this solution on YOUR website!This is an interesting application of the Pythagorean Theorem. The car traveling north can be viewed as going up the y-axis 12 units. The car going east can be be viewed as going to the right along the x-axis. It has traveled 'd' miles. The diagonal from that connects the two cars is the hypotenuse of a right triangle. It's length is d+8, which is given. . 12^2 + d^2 = (d+8)^2 144 + d^2 = d^2 +16d + 64 subtract d^2 from both sides 144 = 16d + 64 subtract 64 from both sides 80 = 16d divide both sides by 16 5 = d d = 5 . Check to ensure diagonal 'c' is 5+8 =13. c^2 = 12^2 + 5^2 c^2 = 144 + 25 c^2 = 169 So, c = 13 Correct. . Answer: The eastbound car has travelled 5 miles. . Done.
 Linear-equations/283289: How to solve: x+y=12 3x-2y=61 solutions Answer 205651 by oberobic(2304)   on 2010-03-20 22:22:15 (Show Source): You can put this solution on YOUR website!You have two equations and two unknowns, so treat them as a system of linear equations: x+y=12 3x-2y=6 . multiply the first equation by 2 and add the two equations together . 2x +2y = 24 3x -2y = 6 5x = 30 x = 6 . x+y=12 y = 12-x = 12-6 = 6 . Check by substituting in the second equation. 3x = 3(6) = 18 -2y = -2(6) = -12 18-12 = 6 Correct . Answer: x = 6 y = 6 . You also can check graphically to see if they two lines cross at (6,6)... . Get the equations into slope-intercept form and define the lines. . x+y=12 y = -x+12 . 3x-2y=6 -2y = -3x +6 y = 3/2x -3 . .
 Polynomials-and-rational-expressions/283296: frank can type a report in 4 hours and james takes 7 hours. how long will it take the two of them typing together?1 solutions Answer 205649 by oberobic(2304)   on 2010-03-20 22:15:02 (Show Source): You can put this solution on YOUR website!Frank works at a rate of 1/4 job per hr. James works at a rate of 1/7 job per hr. It takes them 'x' hours to do one entire job. x*(1/4) + x*(1/7) = 1 . x/4 + x/7 = 1 . 7x + 4x = 28 . 11x = 28 . x = 28/11 = 2.54545 . check by seeing how much of the job each does in 2.54545 hr 2.54545*1/4 = .6363 2.54545*1/7 = .3636 .6363+.3636 = .9999, which is pretty close to 1 whole job . Answer: Working together it takes them 2.54545 hrs. Or about 2 hr 33 min . Done
 Numbers_Word_Problems/283295: 1. the product of two consecutive integers is 600.find the integers.(show working out) 2. the product of two consecutive even integers is 1848.find the integers.(show working out) 3.two positive integers differ by 12 and their product is 405.find the integers.(show working out) topic is quadratic equations1 solutions Answer 205646 by oberobic(2304)   on 2010-03-20 22:07:31 (Show Source): You can put this solution on YOUR website!1. Two consecutive integers are best shown as: x and x+1. (x)(x+1) = 600 x^2 + x -600 = 0 (x+25)(x-24) = 0 x=-25 or x=24 Answer: The two consecutive integers are either 24 & 25 or -25 & -24. ... 2. Two consecutive even integers are best shown as: x and x+2. (x)(x+2) = 1848 x^2+2x-1848 = 0 (x+44)(x-42) = 0 x = -44 or x=42 Answer: The consecutive even integers are either -44 and -42 or 42 and 44. ... 3. Two positive integers differ by 12 is best shown as: x and x+12 (x)(x+12)=405 x^2 + 12x -405 = 0 (x+27)(x-15) = 0 x=-27 or x=15 BUT we are told positive numbers only, x = 15 and x+12 = 27 ... Done
 Quadratic_Equations/283279: Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?1 solutions Answer 205643 by oberobic(2304)   on 2010-03-20 21:59:01 (Show Source): You can put this solution on YOUR website!The Pythagorean theorem applies: the diagonal is the hypotenuse of a right triangle. The sides are the triangle are the length and width of the rectangle. We are told the diagonal is 10 m. . :: The length is 2 m > width, so the width + 2 = length . . substitute . . . . divide through by 2 . . factor . . So our choices are W=-8 and W=6, but a negative width doesn't make sense. . . checking our solution, is the diagonal 10? . . So the Correct . Answer: The lengths of the sides of the rectangle are 6 and 8. . Done.
 Polynomials-and-rational-expressions/283197: The product of 2 consecutive intergers is 41 more than their sum. find the intergers1 solutions Answer 205589 by oberobic(2304)   on 2010-03-20 17:05:21 (Show Source): You can put this solution on YOUR website!Two consecutive numbers can be defined as x and y, but a better choice is x and x+1. . The product of the two numbers is: x(x+1). We are told this 41 more than the sum. The sum of the two numbers is: x + (x+1). . So the equation we need to solve is: . x(x+1) = x+(x+1)+41 . x^2 +x = 2x + 42 . subtract 2x from both sides . x^2 +x -2x = 2x-2x + 42 x^2 -x = 42 . subtract 42 from both sides . x^2 -x -42 = 42-42 = 0 . factor . (x-7)(x+6) = 0 . x = 7 or -6 . We have to check both solutions by substituting these values into the equation. . 7(7+1) = 7+(7+1)+41 ?? 7*8 =56 7+8 + 41=56 Correct . -6(-6+1)=-6+(-6+1)+41 ?? 36 -6 = -6 -6 + 42 ?? 30 = 30 Correct. . Answer the consecutive integers are either 7 and 8 OR -6 and -5. . Done
 Numeric_Fractions/283191: Ok so im on adding and subtracting mixed numbers and Im so confused on how the numerator is changing with the denominator...I dont no if im making sense but here is an example... 9 3/4 + 8 5/6 the numerators changed to 9 9/12 and 8 10/12 so confused I understand how to find everything else but that!1 solutions Answer 205586 by oberobic(2304)   on 2010-03-20 16:50:26 (Show Source): You can put this solution on YOUR website!When you're dealing with fractions you need to get everything to the same denominator. 1/4 + 1/3 cannot be directly added using fractions. The least common multiple of 4 and 3 is 12, so they can have the same denominator of 12. So... . In this case, you're trying to add 9 3/4 + 8 5/6. The least common multiple of 4 and 6 is 12. We can figure this out by multiplying 4*6=24, but we notice that 4=2*2 and 6=2*3, so 12 is the LEAST common multiple. . So... . . But 19/12 is more than 1, it is . . How do we know that 3/4 = 9/12? . Well, remember the idea is the 'least common multiple'. . To change 3/4 to 9/12 you simply look at how many times 4 goes into 12. 12/4 = 3 . So you multiply 3/4 by 3/3 (Remember, you can multiply any number by 1, in this case 1 is 3/3.) . . Similarly, how did 5/6 become 10/12? It is the same process: 12/6 = 2 Multiply 5/6 by 1, which in this case is 2/2. . . Done
 Linear-equations/283026: graph the line containing the given pair of points and find the slope. (5,4),(-4,-3) graph it on a y is -10,10 graph and x is -10 an 10 graph. then find the slope- m=1 solutions Answer 205542 by oberobic(2304)   on 2010-03-20 12:21:20 (Show Source): You can put this solution on YOUR website!The slope-intercept form is: y = mx+b, where m is the slope and b is the y-intercept (the point were x=0). . The slope is defined as the rise over the run, which is the change in 'y' divided by the change in 'x'. . m = (y2-y1)/x2-x1) . (x1,y1) = (5,4) (x2,y2) = (-4,-3) . m = (-3 -4)/(-4-5) m = -7/-9 = 7/9 . y = 7/9x + b . Substitute what we know already to find 'b'. . For example, we know the point (5,4) is on the line. . 4 = 7/9(5) + b . Multiply through by 9 to remove the fraction . 36 = 7(5) + 9b 36 = 35 + 9b 1 = 9b 9b = 1 b = 1/9 . Now we can find the x-intercept, which is the point where y=0. 0 = 7/9x + 1/9 . multiply through by 9 . 9(0) = 7x + 1 0 = 7x + 1 x = -1/7 (-1/7,0) . So, to summarize: Equation is: y = 7/9x + 1/9 y-intercept is: (0, 1/9) x-intercept is: (-1/7, 0) . Graphing it helps confirm your work. . Done