Graphing Linear Functions Practice Worksheet
Practice graphing linear equations using slope, intercepts, and tables of values.
Try graphing each linear function on your own first. Then click Show solution to check the slope, intercepts, key points, and completed graph.
Key Linear Function Ideas
- The slope tells you how steep the line is.
- The \(y\)-intercept is where the line crosses the \(y\)-axis.
- Linear equations graph as straight lines.
- Slope-intercept form is: \[ y=mx+b \]
Level 1: Basic Slope-Intercept Form
Problem 1
Graph the linear function.
Show solution
The slope is \(1\), and the \(y\)-intercept is \(2\).
Key points:
\[ (-2,0),\ (0,2),\ (2,4) \]
Problem 2
Graph the linear function.
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The slope is \(-2\), and the \(y\)-intercept is \(1\).
Key points:
\[ (-1,3),\ (0,1),\ (1,-1) \]
Problem 3
Graph the linear function.
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The slope is \(\frac{1}{2}\), and the \(y\)-intercept is \(-3\).
Key points:
\[ (0,-3),\ (2,-2),\ (4,-1) \]
Level 2: Standard Form
Problem 4
Graph the linear function.
Show solution
Solve for \(y\):
The slope is \(-1\), and the \(y\)-intercept is \(4\).
Key points:
\[ (0,4),\ (2,2),\ (4,0) \]
Problem 5
Graph the linear function.
Show solution
Solve for \(y\):
The slope is \(2\), and the \(y\)-intercept is \(-1\).
Key points:
\[ (0,-1),\ (1,1),\ (2,3) \]
Level 3: Point-Slope Form
Problem 6
Graph the linear function.
Show solution
Compare the equation with point-slope form:
The slope is:
The known point is:
Rewrite the slope as rise over run:
Start at \((1,2)\). Move up \(2\) and right \(1\) to reach another point, \((2,4)\).
Key points:
\[ (1,2),\ (2,4),\ (3,6) \]
As a check, this equation can also be written in slope-intercept form as:
Problem 7
Graph the linear function.
Show solution
Compare the equation with:
The slope is:
Since \(y + 1 = y - (-1)\), the known point is:
Use the slope \(-\frac{3}{2}\): move down \(3\) and right \(2\).
Starting from \((2,-1)\), this gives the point:
You can also move up \(3\) and left \(2\) to reach:
Key points:
\[ (0,2),\ (2,-1),\ (4,-4) \]
In slope-intercept form, the same line is:
Problem 8
Graph the linear function.
Show solution
Compare the equation with:
The slope is:
The expression \(x + 4\) is really \(x - (-4)\), so the known point is:
Use the slope \(\frac{1}{2}\): move up \(1\) and right \(2\).
Starting from \((-4,3)\), this gives:
Repeat the same rise and run to reach:
Key points:
\[ (-4,3),\ (-2,4),\ (0,5) \]
In slope-intercept form, the same line is:
More Linear Function Resources
Use the guide for a full explanation, explore graphs dynamically in the Graphing Lab, or practice individual linear-function skills with step-by-step feedback.
Graphing Linear Functions Guide
Review slope, intercepts, slope-intercept form, point-slope form, and several ways to graph a line.
Graphing Lab
Enter equations and explore how slope, intercepts, and equation changes affect a graph.
Slope Guide
Review rise over run, positive and negative slope, and finding slope from two points.
Slope Practice
Practice finding and interpreting slope with guided interactive problems.
Slope-Intercept Form Guide
Learn how \(m\) and \(b\) determine the graph of \(y=mx+b\).
Slope-Intercept Form Practice
Identify slope and intercepts, build equations, and connect equations with graphs.
Point-Slope Form Guide
Learn how a slope and one known point can be used to write and graph a line.
Point-Slope Form Practice
Practice identifying, writing, graphing, and converting point-slope equations.
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