SOLUTION: 1. What is the equation of a line that passes through points (-1, 2) and (5, 2)? y - 2 = 0 x - 2 = 0 y - x - 2 = 0 2. What is the equation of a line with a slope of -2 and

Algebra ->  Graphs -> SOLUTION: 1. What is the equation of a line that passes through points (-1, 2) and (5, 2)? y - 2 = 0 x - 2 = 0 y - x - 2 = 0 2. What is the equation of a line with a slope of -2 and       Log On


   

Question 399387: 1. What is the equation of a line that passes through points (-1, 2) and (5, 2)?
y - 2 = 0
x - 2 = 0
y - x - 2 = 0
2. What is the equation of a line with a slope of -2 and a y-intercept of 8?
x + 2y - 8 = 0
2x + y - 8 = 0
2x - y + 8 = 0
3. What is the slope of a line parallel to the line whose equation is y - x = 5?
-1
1
5
4. What is the equation of the line that passes through the point (1, 1) and has a y-intercept of 2.
x - y + 2 = 0
x + y - 2 = 0
x - y - 2 = 0
5. The slope of a line is 1/3 . What is the slope of a line perpendicular to this line?
-3
-1/3
1/3
3
6. What is the slope of a line perpendicular to the line whose equation is y = 2x + 5?
slope = -1
slope = -1/2
slope = -2
7. What is the equation of a line with a point (-3, 0) and no slope?
x + 3 = 0
y + 3 = 0
x - 3 = 0
y - 3 = 0
8. What is the equation of a line that passes through point (1, -2) and has a slope of 1/3 .
3x - y - 7 = 0
x - 3y + 7 = 0
x - 3y - 7 = 0
9. What is the equation of the line whose y-intercept is 3 and slope is 1?
y = x - 3
y = x + 3
y = 3x + 1
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

1. What is the equation of a line that passes through points (-1, 2) and (5, 2) y = 2

7. What is the equation of a line with a point (-3, 0) and no slope? x = -3

 

  

2. What is the equation of a line with a slope of -2 and a y-intercept of 8?

  y = -2x + 8

3. What is the slope of a line parallel to the line whose equation is y - x = 5?

 y = x+ 5   parallel lines have equal slopes of m = 1

4. What is the equation of the line that passes through the point (1, 1) and has a y-intercept of 2.  

y = mx + 2  

1 = m + 2    m = -1

y = -x + 2

5. The slope of a line is 1/3 . What is the slope of a line perpendicular to this line? 

⊥ Lines have slopes that are negative reciprocals of one another:  m = - 3/1

6. What is the slope of a line perpendicular to the line whose equation is y = 2x + 5?  m =  -1/2

8. What is the equation of a line that passes through point (1, -2) and has a slope of 1/3 . 

y = (1/3)x + b

-2 = 1/3 + b

 -7/3 = b

y = (1/3)x -7/3

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1.
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-1,2) and (5,2)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (-1,2) and (x%5B2%5D,y%5B2%5D) is the second point (5,2))


m=%282-2%29%2F%285--1%29 Plug in y%5B2%5D=2,y%5B1%5D=2,x%5B2%5D=5,x%5B1%5D=-1 (these are the coordinates of given points)


m=+0%2F6 Subtract the terms in the numerator 2-2 to get 0. Subtract the terms in the denominator 5--1 to get 6




m=0 Reduce



So the slope is

m=0





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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-2=%280%29%28x--1%29 Plug in m=0, x%5B1%5D=-1, and y%5B1%5D=2 (these values are given)



y-2=%280%29%28x%2B1%29 Rewrite x--1 as x%2B1



y-2=0x%2B%280%29%281%29 Distribute 0


y-2=0x%2B0 Multiply 0 and 1 to get 0%2F0. Now reduce 0%2F0 to get 0

y=0x%2B0%2B2 Add 2 to both sides to isolate y


y=0x%2B2 Combine like terms 0 and 2 to get 2

------------------------------------------------------------------------------------------------------------

Answer:



So the equation of the line which goes through the points (-1,2) and (5,2) is:y=0x%2B2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=0 and the y-intercept is b=2


Notice if we graph the equation y=0x%2B2 and plot the points (-1,2) and (5,2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=0x%2B2 through the points (-1,2) and (5,2)


Notice how the two points lie on the line. This graphically verifies our answer.





answer: y+-+x+-+2+=+0 or in slope-intercept form y+=+x+%2B+2

2.
Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out:

  • it goes through point (0, 8)

  • it has a slope of -2



First, let's draw a diagram of the coordinate system with point (0, 8) plotted with a little blue dot:



Write this down: the formula for the equation, given point x%5B1%5D%2C+y%5B1%5D and intercept a, is

y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 (see a paragraph below explaining why this formula is correct)

Given that a=-2, and system%28+x%5B1%5D+=+0%2C+y%5B1%5D+=+8+%29+, we have the equation of the line:

y=-2%2Ax+%2B+8

Explanation: Why did we use formula y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (x%5B1%5D, y%5B1%5D) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (x%5B1%5D, y%5B1%5D): y%5B1%5D+=+a%2Ax%5B1%5D%2Bb Here, we know a, x%5B1%5D, and y%5B1%5D, and do not know b. It is easy to find out: b=y%5B1%5D-a%2Ax%5B1%5D. So, then, the equation of the line is: +y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+.

Here's the graph:





answer: 2x+%2B+y+-+8+=+0 or in slope-intercept form y+=-2x%2B8

3.
y+-+x+=+5 or -+x+%2B+y+=+5

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -1+x+%2B+1+y+=+5 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--1%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 5/-1 = -5.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 5/1 = 5.
  • Slope is --1/1 = 1.
  • Equation in slope-intercept form: y=1*x+5.
graph%28+500%2C+500%2C+-5-8%2C+-5%2B8%2C+5-8%2C+5%2B8%2C+1%2Ax%2B5+%29+


answer: slope is -a%2Fb=+-%28-1%29%2F1=1

4.
Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (1, 1) and (x2, y2) = (0, 2).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%282-1%29%2F%280-1%29+=+-1.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or -1%2A1+%2Bb+=+2. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=1--1%2A1+=+2.

y=(-1)x + (2)

Your graph:





answer: x+%2B+y+-+2+=+0or in slope-intercept form y+=-x%2B2


5.
if slope of the one line is m, the slope of perpendicular line will be m1=-%281%2Fm%29

so, if m=1%2F3, the slope of perpendicular line will be m1=-%281%2F%281%2F3%29%29=-3

6.
equation +y+=+2x+%2B+5 is already in slope-intercept form and you can see that slope is 2; so, the slope of a line perpendicular to this line will be -%281%2F2%29

7.

Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out:

  • it goes through point (-3, 0)

  • it has a slope of 0



First, let's draw a diagram of the coordinate system with point (-3, 0) plotted with a little blue dot:



Write this down: the formula for the equation, given point x%5B1%5D%2C+y%5B1%5D and intercept a, is

y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 (see a paragraph below explaining why this formula is correct)

Given that a=0, and system%28+x%5B1%5D+=+-3%2C+y%5B1%5D+=+0+%29+, we have the equation of the line:

y=0%2Ax+%2B+0

Explanation: Why did we use formula y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (x%5B1%5D, y%5B1%5D) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (x%5B1%5D, y%5B1%5D): y%5B1%5D+=+a%2Ax%5B1%5D%2Bb Here, we know a, x%5B1%5D, and y%5B1%5D, and do not know b. It is easy to find out: b=y%5B1%5D-a%2Ax%5B1%5D. So, then, the equation of the line is: +y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+.

Here's the graph:





8.
the equation of a line that passes through point (1, -2) and has a slope of 1/3

Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out:

  • it goes through point (1, -2)

  • it has a slope of 0.333333333333333



First, let's draw a diagram of the coordinate system with point (1, -2) plotted with a little blue dot:



Write this down: the formula for the equation, given point x%5B1%5D%2C+y%5B1%5D and intercept a, is

y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 (see a paragraph below explaining why this formula is correct)

Given that a=0.333333333333333, and system%28+x%5B1%5D+=+1%2C+y%5B1%5D+=+-2+%29+, we have the equation of the line:

y=0.333333333333333%2Ax+%2B+-2.33333333333333

Explanation: Why did we use formula y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (x%5B1%5D, y%5B1%5D) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (x%5B1%5D, y%5B1%5D): y%5B1%5D+=+a%2Ax%5B1%5D%2Bb Here, we know a, x%5B1%5D, and y%5B1%5D, and do not know b. It is easy to find out: b=y%5B1%5D-a%2Ax%5B1%5D. So, then, the equation of the line is: +y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+.

Here's the graph:




you got:
3x+-+y+-+7+=+0...or in slope-intercept form y=3x-7
x+-+3y+%2B+7+=+0...or in slope-intercept form 3y=-x-7
ory=-%281%2F3%29x-7%2F3

x+-+3y+-+7+=+0+...or in slope-intercept form 3y=x-7 ory=%0D%0A%0D%0A%281%2F3%29x-7%2F3
so the answer is : y=%281%2F3%29x+-+7%2F3
9.
Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out:

  • it goes through point (0, 3)

  • it has a slope of 1



First, let's draw a diagram of the coordinate system with point (0, 3) plotted with a little blue dot:



Write this down: the formula for the equation, given point x%5B1%5D%2C+y%5B1%5D and intercept a, is

y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 (see a paragraph below explaining why this formula is correct)

Given that a=1, and system%28+x%5B1%5D+=+0%2C+y%5B1%5D+=+3+%29+, we have the equation of the line:

y=1%2Ax+%2B+3

Explanation: Why did we use formula y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (x%5B1%5D, y%5B1%5D) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (x%5B1%5D, y%5B1%5D): y%5B1%5D+=+a%2Ax%5B1%5D%2Bb Here, we know a, x%5B1%5D, and y%5B1%5D, and do not know b. It is easy to find out: b=y%5B1%5D-a%2Ax%5B1%5D. So, then, the equation of the line is: +y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+.

Here's the graph:





so the answer is : y+=+x+%2B+3