Work with linear equations in forms such as Ax+By=C and y=mx+b. | Linear equations in two variables | SAT Math

Convert between line forms to reveal slope, intercepts, or a known point.

Core Idea

Every linear equation can be written in slope-intercept form $𝑦 = 𝑚 𝑥 + 𝑏$ , standard form $𝐴 𝑥 + 𝐵 𝑦 = 𝐶$ , or point-slope form $𝑦 - 𝑦 1 = 𝑚 (𝑥 - 𝑥 1)$ . Converting between forms is just algebraic rearrangement — the line itself doesn't change.

Understanding

The three forms describe the same line but spotlight different features. Slope-intercept $𝑦 = 𝑚 𝑥 + 𝑏$ shows the slope $𝑚$ and the y-intercept $𝑏$ directly. Standard form $𝐴 𝑥 + 𝐵 𝑦 = 𝐶$ makes it easy to find both intercepts by setting one variable to zero. Point-slope $𝑦 - 𝑦 1 = 𝑚 (𝑥 - 𝑥 1)$ is built from a known point and slope.

To convert from standard to slope-intercept, isolate $𝑦$ : subtract the $𝑥$ -term, then divide by the coefficient of $𝑦$ . To go the other direction, clear fractions and move all variable terms to one side.

On the SAT, you'll often need to identify which form a given equation is in, or rewrite an equation to reveal specific information — like the slope or y-intercept — that a question asks about.

Step by Step

Identify which form the equation is currently in.
Decide what information you need (slope, intercept, or a specific point).
Rearrange algebraically: isolate y for slope-intercept, or move all terms to one side for standard form.
Simplify and check that the equation still represents the same line by substituting a known point.

Misconceptions

Forgetting to divide every term by the coefficient of y when converting to slope-intercept form — this changes the slope and intercept.
Thinking standard form requires A to be positive. While convention prefers it, SAT answer choices may not follow this convention.
Confusing the sign of the slope when rearranging: moving $3 𝑥$ from the left side means subtracting it, giving $- 3 𝑥$ on the other side.

Question

Worked Example

Which of the following is equivalent to $4 𝑥 - 2 𝑦 = 10$ written in slope-intercept form?

Select an answer to see the explanation