SAT Topic 2

Linear equations in 2 variables

Slope-intercept form, standard form, intercepts, and how they show up on a graph.

Concept

A linear equation in two variables describes a straight line in the x-y plane. The two most common forms on the SAT:

Slope-intercept form: y = mx + b — m is the slope (steepness), b is the y-intercept (where the line crosses the y-axis).
Standard form: Ax + By = C — useful for finding intercepts quickly: set x = 0 for the y-intercept, y = 0 for the x-intercept.

You should be able to read either form, convert between them, and pick out the slope and the two intercepts in seconds.

Solution

Step 1. Move the x term: −2y = −4x + 8

Step 2. Divide every term by −2: y = 2x − 4

Slope m = 2. y-intercept (0, −4).

Solution

y-int. Let x = 0 ⇒ 5y = 15 ⇒ y = 3. Point (0, 3).

x-int. Let y = 0 ⇒ 3x = 15 ⇒ x = 5. Point (5, 0).

Slope. 0 − 35 − 0 = −35

Plot (0, 3) and (5, 0) and draw the line. It slopes downward at −3/5.

8 questions on slope-intercept form, standard form, and intercepts. Instant feedback after each answer.

Practice test · 8 questions Question 1 of 8 · Score 0