McGraw-Hill Education GRE 2019

Using Two Points to Determine a Line

Generally, if the GRE asks you to determine the equation for a line, it will do so by

providing you with two points. Let’s look at how to do so:

What is the equation for the line that passes through (2,11) and (5,20)?

Step 1: Use the slope formula to determine m:

y 2 – y 1

x 2 – x 1 =

20 – 11

5 – 2 =

9

3 = 3

Step 2: Substitute the value for m in the equation for the line:

y = 3x + b

Step 3: Solve for b: Since (2,11) and (5,20) lie on the line, both points will

satisfy the equation for the line. Thus you can plug in the coordinates for

either point to solve for b. Use the point (2,11):

11 = 3(2) + b

b = 5

Step 4: Substitute b into the equation:

y = 3x + 5

Using a Line to Determine a Point

In the previous example, you used two points on a line to determine its equation.

In other situations, you will be given the equation for a line and will be asked to

find a point that lies on the line. Let’s look at an example:

If line k is defined by the equation y = 7x + 3, then which of the following

points must lie on the line?

A (3,7)

B (7, 3)

C (3,0)

D (2,17)

E (17, 2)

434 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 434 12/05/17 12:06 pm