GRE Math : How to find the equation of parallel lines

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Example Question #1 : Coordinate Geometry

If the line through the points (5, –3) and (–2, p) is parallel to the line y = –2x – 3, what is the value of p ?

Possible Answers:

–10

–17

Correct answer:

Explanation:

Since the lines are parallel, the slopes must be the same. Therefore, (p+3) divided by (–2–5) must equal –2. 11 is the only choice that makes that equation true. This can be solved by setting up the equation and solving for p, or by plugging in the other answer choices for p.

$\frac{p--3}{-2-5}=\frac{p+3}{-2-5}=-2$

$\frac{p+3}{-7}=-2$

$(\frac{p+3}{-7})-7=-2(-7)$

p+3=14

p=11

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Example Question #11 : Coordinate Geometry

Which of these formulas could be a formula for a line perpendicular to the line 2x + 3y = 16 ?

Possible Answers:

6y - 9x = 16.5

6y + 9x = 16

4x + 6y = 24

4y - 9x = 24

3y - 4x = 23

Correct answer:

6y - 9x = 16.5

Explanation:

This is a two-step problem. First, the slope of the original line needs to be found. The slope will be represented by "" when the line is in -intercept form (y=mx+b) .

2x +3y = 16

3y = -2x +16

$y = \left(\frac{-2}{3}\right)x +\left(\frac{16}{3}\right)$

So the slope of the original line is $-\frac{2}{3}$ . A line with perpendicular slope will have a slope that is the inverse reciprocal of the original. So in this case, the slope would be $\frac{3}{2}$ . The second step is finding which line will give you that slope. For the correct answer, we find the following:

6y - 9x = 16.5

6y = 9x +16.5

$y= \left(\frac{3}{2}x\right) +\left(\frac{16.5}{6}\right)$

So, the slope is $\frac{3}{2}$ , and this line is perpendicular to the original.

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Example Question #11 : How To Find The Equation Of Parallel Lines

What is the equation for the line running through (-3,-7) and parallel to 15x +5y=105 ?

Possible Answers:

y=-3x-16

y=5x+21

y=-6x-3

y=-5x-21

y=21x+5

Correct answer:

y=-3x-16

Explanation:

To begin, solve the given equation for . This will give you the slope-intercept form of the line.

5y=-15x+105

Divide everything by $5$ :

y=-3x+21

Therefore, the slope of the line is .

Now, for a point (a,b) , the point-slope form of a line is:

y-b=m(x-a) , where is the slope

For our point, this is:

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

This is the same as:

y+7=-3(x+3)

Distribute and solve for :

y+7=-3x-9

y=-3x-16

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GRE Math : How to find the equation of parallel lines

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : Coordinate Geometry

Example Question #11 : Coordinate Geometry

Example Question #11 : How To Find The Equation Of Parallel Lines

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