The coefficient of x tells how much y changes when x increases by 1.
Free Interactive Algebra Tool
Slope-Intercept Form Practice
Learn how to use y = mx + b to identify slope and y-intercept, interpret linear equations, build equations, and connect equations to graphs.
Start practicingNeed Help With Slope-Intercept Form?
Review y = mx + b, how to identify slope and y-intercept, how each value changes a graph, and how to write linear equations in slope-intercept form.
Read the Slope-Intercept Form Guide
Practice Mode
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Problem 1 of 10
10%
Current Problem
Identify the slope and y-intercept.
Identify m & b
Beginner
Problem
y = 3x + 5
1
Find m
2
Find b
3
Interpret
Step 1
Find the slope
In y = mx + b, the coefficient of x is m.
y = 3x + 5
Step 1
Interpret the slope
Decide what the value of m tells you about the line.
y = -2x + 4
Step 1
Place the slope into the equation
Use the given values of m and b to build y = mx + b.
Slope
m = 2
Y-Intercept
b = -3
Step 1
Study the graph
Identify the y-intercept and slope, then choose the equation that matches the graph.
Slope
?
Y-Intercept
?
In y = mx + b, start by finding the coefficient of x.
Hint
In y = mx + b, m is the coefficient multiplying x.
Slope-Intercept Form Reference
y = mx + b
Slope-intercept form describes a line using its slope and where it crosses the y-axis.
The line crosses the y-axis at the point whose x-coordinate is 0.
The line rises as you move from left to right.
The line falls as you move from left to right.
If m = 0, the line is horizontal.
A fraction such as 2/3 means rise 2 units for every run of 3 units.
Problem Complete
y = 3x + 5
The slope is 3 and the y-intercept is (0, 5).
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You completed all 10 slope-intercept form problems.
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m tells you the slope
The coefficient of x describes the line's rate of change and whether it rises or falls from left to right.
b tells you where to start
The y-intercept is the point (0, b), where the line crosses the vertical axis.
Together they determine the line
The values of m and b completely determine a nonvertical line written in slope-intercept form.
Example
How do you read y = -2x + 5?
Compare the equation with the general form y = mx + b.
y = -2x + 5
1
Identify m
m = -2
2
Identify b
b = 5
3
Interpret the graph
The line crosses at (0, 5) and falls 2 units
for every 1 unit it moves right.
The negative slope tells us the line falls from left to right, while b = 5 tells us the line crosses the y-axis at (0, 5).
Practice Slope-Intercept Form Step by Step
Slope-intercept form is one of the most common ways to write a linear equation. It is written as y = mx + b, where m represents the slope and b represents the y-intercept.
This interactive slope-intercept form practice tool helps students connect the equation to the behavior and graph of a line instead of simply memorizing what the letters mean.
Identify the Slope in y = mx + b
The value of m is the coefficient multiplying x. Positive values of m produce lines that rise from left to right, negative values produce lines that fall, and m = 0 produces a horizontal line.
Identify the Y-Intercept
The value of b tells where the line crosses the y-axis. Because every point on the y-axis has x = 0, the y-intercept is written as the ordered pair (0, b).
Write an Equation From Slope and Y-Intercept
When the slope and y-intercept are known, substitute their values for m and b in y = mx + b. Pay careful attention to negative signs and coefficients such as 1, -1, and fractional slopes.
Match Linear Equations to Graphs
A graph can be matched to an equation by first locating its y-intercept and then checking its slope. The interactive graphing problems reinforce the connection between the symbolic equation and the visual line.
Three Difficulty Levels
Beginner problems emphasize simple integer slopes and y-intercepts. Intermediate practice introduces negative values, invisible coefficients, and fractional slopes. Advanced problems combine more challenging coefficients, graph interpretation, and mixed representations.
Build a Foundation for Linear Equations
Understanding slope-intercept form prepares students for graphing linear equations, writing equations from points, point-slope form, parallel and perpendicular lines, and systems of linear equations.