SAT Math glossary

Slope-Intercept Form

Slope‑intercept form is a line's equation written as .

Example

Graph a line from its y‑intercept and slope

Plot $(0, b)$ first. To find another point, go $1$ right and add $m$ to the y‑coordinate.

Click the point where this line crosses the y-axis.

Counterexample

The number multiplying $x$ is not always the slope

In $6x + 2y = 14$ , $y$ is not alone on one side. Solve for $y$ to find the slope and y‑intercept.

Concept practice

What is the slope of the line $10x + 5y = 20$ ?

Special cases

Slope‑intercept form fits every line except vertical lines

A line with negative slope falls from left to right
From $(0, 5)$ , the line goes $2$ down for every $1$ right.
Zero slope gives a horizontal line
In $y = 0x + 4$ , changing $x$ leaves $y$ at $4$ .
A zero y‑intercept puts the line through the origin
$y = 3x$ passes through $(0, 0)$ because its y‑intercept is $0$ .
A vertical line has no slope‑intercept form
Every point on $x = 2$ has the same x‑coordinate. There is no step to the right along the line, so its slope is undefined.

Concept practice

What is the slope of the line $5y = 30$ ?

On the SAT

Use slope and y‑intercept to model costs, read graphs, compare lines, and count solutions

In a word problem, $m$ is the rate and $b$ is the starting amount

A repair costs $C$ dollars for $h$ hours of work.

From a graph, read $b$ on the y‑axis and $m$ as rise over run

the line crosses the y-axis at

(0, 4)

up 2 for every 3 right

Compare slopes to tell parallel lines from perpendicular lines

Equal slopes and different y‑intercepts mean parallel lines

For nonvertical lines, perpendicular slopes multiply to $-1$

Compare slopes and y‑intercepts to count a system's solutions

Different slopesExactly one solution
Same slope, different y‑interceptsNo solution
Same slope and y‑interceptInfinitely many solutions

Concept practice

$y = 3x + 5$ $6x - 2y = -10$ How many solutions does the given system of linear equations have?

Connected terms

Slope‑intercept form connects to slope, standard form, and comparing lines

Parts of slope‑intercept form

slopeUse $m$ to find another point from the y‑intercept.
y-interceptPlot $(0, b)$ first when graphing from slope‑intercept form.

Another way to write the line

standard formFor lines that are not vertical, solving for $y$ gives slope‑intercept form.

Compare slopes and y‑intercepts

parallelEqual $m$ values with different $b$ values give parallel lines.
perpendicularIf $m \ne 0$ , a perpendicular line has slope $-\frac{1}{m}$ .
system of equationsCompare $m$ and $b$ to count the system's solutions.

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Lessons that take this page further

Equations of LinesMath · Linear Relationships
Parallel and Perpendicular LinesMath · Linear Relationships
Systems of EquationsMath · Linear Relationships
Linear ModelingMath · Linear Relationships

Sources

Checked against these sources on October 13, 2026.

Graph a line from its y‑intercept and slope

The number multiplying xxx is not always the slope

Slope‑intercept form fits every line except vertical lines

A line with negative slope falls from left to right

Zero slope gives a horizontal line

A zero y‑intercept puts the line through the origin

A vertical line has no slope‑intercept form

Use slope and y‑intercept to model costs, read graphs, compare lines, and count solutions

In a word problem, mmm is the rate and bbb is the starting amount

From a graph, read bbb on the y‑axis and mmm as rise over run

Compare slopes to tell parallel lines from perpendicular lines

Equal slopes and different y‑intercepts mean parallel lines

For nonvertical lines, perpendicular slopes multiply to −1-1−1

Compare slopes and y‑intercepts to count a system's solutions

Slope‑intercept form connects to slope, standard form, and comparing lines

Build SAT math skills and test-day stamina

Sources

The number multiplying $x$ is not always the slope

In a word problem, $m$ is the rate and $b$ is the starting amount

From a graph, read $b$ on the y‑axis and $m$ as rise over run

For nonvertical lines, perpendicular slopes multiply to $-1$