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Linear_Algebra/124795: This question is from textbook Algebra 2
Write an equation for the line containing the indicated points.
(-6,-6) and (-3,1)
1 solutions

Answer 91483 by jim_thompson5910(28593)   on 2008-02-04 16:35:05 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Finding the Equation of a Line First lets find the slope through the points (,) and (,) Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,)) Plug in ,,, (these are the coordinates of given points) Subtract the terms in the numerator to get . Subtract the terms in the denominator to get So the slope is ------------------------------------------------ Now let's use the point-slope formula to find the equation of the line: ------Point-Slope Formula------ where is the slope, and (,) is one of the given points So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Rewrite as Rewrite as Distribute Multiply and to get . Now reduce to get Subtract from both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line which goes through the points (,) and (,) is: The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver) Graph of through the points (,) and (,) Notice how the two points lie on the line. This graphically verifies our answer.

 Graphs/124727: Please help solve: -2x+3y=-2 y=3x-31 solutions Answer 91435 by jim_thompson5910(28593)   on 2008-02-03 23:07:05 (Show Source): You can put this solution on YOUR website! Start with the given system Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute Combine like terms on the left side Add 9 to both sides Combine like terms on the right side Divide both sides by 7 to isolate x Divide Now that we know that , we can plug this into to find Substitute for each Simplify So our answer is and which also looks like Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer. Graph of (red) and (green)
 Graphs/124725: graph the line with the slope 2/3 passing through the point (-2,1)1 solutions Answer 91433 by jim_thompson5910(28593)   on 2008-02-03 22:56:35 (Show Source): You can put this solution on YOUR website! If you want to find the equation of line with a given a slope of which goes through the point (,), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula--- where is the slope, and is the given point So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Rewrite as Distribute Multiply and to get Add 1 to both sides to isolate y Combine like terms and to get (note: if you need help with combining fractions, check out this solver) ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line with a slope of which goes through the point (,) is: which is now in form where the slope is and the y-intercept is Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver) Graph of through the point (,) and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
 Graphs/124724: graph the inequality 3x-4y>-321 solutions Answer 91432 by jim_thompson5910(28593)   on 2008-02-03 22:55:56 (Show Source): You can put this solution on YOUR website!In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (note: if you need help with graphing, check out this solver) graph of Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,0) into the inequality Plug in and Simplify (note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.) Since this inequality is true, we simply shade the entire region that contains (0,0) Graph of with the boundary (which is the line in red) and the shaded region (in green) (note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
 Graphs/124723: graph the inequality 4x+5y<161 solutions Answer 91431 by jim_thompson5910(28593)   on 2008-02-03 22:55:12 (Show Source): You can put this solution on YOUR website!In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (note: if you need help with graphing, check out this solver) graph of Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,0) into the inequality Plug in and Simplify Since this inequality is true, we simply shade the entire region that contains (0,0) Graph of with the boundary (which is the line in red) and the shaded region (in green) (note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
 Graphs/124722: graph the line with the slope -4 ppassing through the point (2,-1)1 solutions Answer 91430 by jim_thompson5910(28593)   on 2008-02-03 22:54:23 (Show Source): You can put this solution on YOUR website! If you want to find the equation of line with a given a slope of which goes through the point (,), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula--- where is the slope, and is the given point So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Rewrite as Distribute Multiply and to get Subtract 1 from both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line with a slope of which goes through the point (,) is: which is now in form where the slope is and the y-intercept is Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver) Graph of through the point (,) and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
 Graphs/124720: Graph f(x) = 3x + 2. THIS IS REALLY GIVING ME PROBLEMS TRYING TO GRAPH THIS EQUASTION.1 solutions Answer 91422 by jim_thompson5910(28593)   on 2008-02-03 22:21:43 (Show Source): You can put this solution on YOUR website! Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 3 and the run is 1. This means that to go from point to point, we can go up 3 and over 1 So starting at , go up 3 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Graphs/124719: Graph the inequality. 1 solutions Answer 91420 by jim_thompson5910(28593)   on 2008-02-03 22:19:35 (Show Source): You can put this solution on YOUR website!In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (note: if you need help with graphing, check out this solver) graph of Now lets pick a test point, say (0,1). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,1) into the inequality Plug in and Simplify Since this inequality is not true, we do not shade the entire region that contains (0,1). So this means we shade the region that is on the opposite side of the line Graph of with the boundary (which is the line in red) and the shaded region (in green)
 Graphs/124718: Solve the system by graphing. x – 2y = 8 x + y = –1 REALLY NEED HELP GRAPHING!1 solutions Answer 91419 by jim_thompson5910(28593)   on 2008-02-03 22:18:38 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: In order to graph these equations, we need to solve for y for each equation. So let's solve for y on the first equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets graph (note: if you need help with graphing, check out this solver) Graph of So let's solve for y on the second equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets add the graph of to our first plot to get: Graph of (red) and (green) From the graph, we can see that the two lines intersect at the point (,) (note: you might have to adjust the window to see the intersection)
 Graphs/124717: Solve the system by substitution. 2x – 4y = 18 y = –x – 12 1 solutions Answer 91418 by jim_thompson5910(28593)   on 2008-02-03 22:17:28 (Show Source): You can put this solution on YOUR website!Start with the given system Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute Combine like terms on the left side Subtract 48 from both sides Combine like terms on the right side Divide both sides by 6 to isolate x Divide Now that we know that , we can plug this into to find Substitute for each Simplify So our answer is and which also looks like Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer. Graph of (red) and (green)
 decimal-numbers/124702: write 1/300 using sientifc notation. i feel stupid for this but oh well.1 solutions Answer 91416 by jim_thompson5910(28593)   on 2008-02-03 22:12:15 (Show Source): You can put this solution on YOUR website!First divide to get 0.00333333333333 which rounds to 0.0033 Place a decimal between the first digit 3 and the second digit 3. Now how many spots to the left must the decimal move to go from the number to the number ? The decimal needs to move 3 places to the left. So this is equivalent to multiplying by to move the decimal 3 places to the left. Notice how the exponent -3 corresponds to the number of spots the decimal needs to move. So putting all of this information together, we get This means that the number in scientific notation is In other words, So this also means that the approximate value for is
 Linear-systems/124713: The sum of two numbers is 52. Twice the first number is 17 more than the second. Find the numbers. I just need to know how to set this up.1 solutions Answer 91415 by jim_thompson5910(28593)   on 2008-02-03 22:05:43 (Show Source): You can put this solution on YOUR website!The sentence "The sum of two numbers is 52" translates to The sentence "Twice the first number is 17 more than the second" translates to So you get the system
 Graphs/124698: Solve the system by graphing. x – 2y = 8 x + y = –1 1 solutions Answer 91414 by jim_thompson5910(28593)   on 2008-02-03 22:02:47 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: In order to graph these equations, we need to solve for y for each equation. So let's solve for y on the first equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets graph (note: if you need help with graphing, check out this solver) Graph of So let's solve for y on the second equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets add the graph of to our first plot to get: Graph of (red) and (green) From the graph, we can see that the two lines intersect at the point (,) (note: you might have to adjust the window to see the intersection)
 Graphs/124711: graph the inequality 2x+y<-91 solutions Answer 91413 by jim_thompson5910(28593)   on 2008-02-03 21:59:51 (Show Source): You can put this solution on YOUR website!In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (note: if you need help with graphing, check out this solver) graph of Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,0) into the inequality Plug in and Simplify (note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.) Since this inequality is not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line Graph of with the boundary (which is the line in red) and the shaded region (in green) (note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
 Graphs/124710: graph the inequality -x-y<81 solutions Answer 91412 by jim_thompson5910(28593)   on 2008-02-03 21:58:50 (Show Source): You can put this solution on YOUR website!In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (note: if you need help with graphing, check out this solver) graph of Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,0) into the inequality Plug in and Simplify (note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.) Since this inequality is true, we simply shade the entire region that contains (0,0) Graph of with the boundary (which is the line in red) and the shaded region (in green) (note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
 Graphs/124709: graph the line with slope 4 passing through the point (4,2)1 solutions Answer 91411 by jim_thompson5910(28593)   on 2008-02-03 21:57:52 (Show Source): You can put this solution on YOUR website! If you want to find the equation of line with a given a slope of which goes through the point (,), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula--- where is the slope, and is the given point So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Distribute Multiply and to get Add 2 to both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line with a slope of which goes through the point (,) is: which is now in form where the slope is and the y-intercept is Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver) Graph of through the point (,) and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
 Equations/124706: t/9-7=-51 solutions Answer 91409 by jim_thompson5910(28593)   on 2008-02-03 21:48:51 (Show Source): You can put this solution on YOUR website! Start with the given equation Multiply both sides by the LCM of 9. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver) Distribute and multiply the LCM to each side Add 63 to both sides Combine like terms on the right side -------------------------------------------------------------- Answer: So our answer is
 Graphs/124700: Solve the system by substitution. 2x – 4y = 18 y = –x – 12 1 solutions Answer 91407 by jim_thompson5910(28593)   on 2008-02-03 21:38:44 (Show Source): You can put this solution on YOUR website!Start with the given system Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute Combine like terms on the left side Subtract 48 from both sides Combine like terms on the right side Divide both sides by 6 to isolate x Divide Now that we know that , we can plug this into to find Substitute for each Simplify So our answer is and which also looks like Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer. Graph of (red) and (green)
 Equations/124703: Write the equation of the line with slope –7 and y-intercept (0, 5).1 solutions Answer 91406 by jim_thompson5910(28593)   on 2008-02-03 21:35:08 (Show Source): You can put this solution on YOUR website! If you want to find the equation of line with a given a slope of which goes through the point (,), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula--- where is the slope, and is the given point So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Distribute Multiply and to get Add 5 to both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line with a slope of which goes through the point (,) is: which is now in form where the slope is and the y-intercept is Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver) Graph of through the point (,) and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
 Inequalities/124677: Find the solution set 1 solutions Answer 91382 by jim_thompson5910(28593)   on 2008-02-03 19:37:08 (Show Source): You can put this solution on YOUR website! Start with the given compound inequality Multiply all sides by the LCD 10. This will eliminate the fractions Distribute and multiply Distribute again Add 24 to all sides Divide every side by 12 to isolate x. Reduce. So the solution in interval notation is: (,] Now let's graph the solution set Note: at there is a open circle (which means this point is excluded) and at there is a closed circle (which means this point is included)
 Travel_Word_Problems/124676: A girl walked from her home into town at the rate of 4 miles per hour. She returned by bus over the same route. The bus averaged 20 miles per hour, and the entire round trip took 1 hour and 40 minutes, including the 10 minute wait for the bus. How far did the girl walk? 1 solutions Answer 91381 by jim_thompson5910(28593)   on 2008-02-03 19:34:37 (Show Source): You can put this solution on YOUR website!Let =walking time and =driving time Now we're going to use the distance-rate-time equation Since the walking speed is 4 mph and the walking time is , this means and Plug in and Also, since the driving speed is 20 mph and the driving time is , this means and Plug in and Because the distance is the same both ways, this means that Start with the given equation Divide both sides by 4 to isolate If the entire trip took 1 hour and 40 minutes and there was a 10 minute wait, then the traveling portion took 1 hour and 30 minutes (which is 1.5 hours) So the sum of these two times is 1.5. In other words, we have this first equation Plug in Combine like terms Divide both sides by 6 to isolate So the driving time is 0.25 hours or 15 minutes Now let's go back to the equation Start with the given equation Plug in our answer Multiply So the distance that she traveled is 5 miles