Pre-Algebra
Functions (introductory)
Graphing linear equations (slope-intercept form)
20 practice questions
0 video lessons
Theory + worked examples
Graphing Linear Equations (Slope-Intercept Form)
California Pre-Algebra • Standard 8.EE.6 • Functions
Graphing Linear Equations (Slope-Intercept Form) is a topic in Functions in the California Common Core State Standards. It is aligned to Standard 8.EE.6, which requires students to graph linear equations using slope-intercept form.
Slope-intercept form \(y=mx+b\) lets you graph a line by plotting the \(y\)-intercept and using the slope.
Theory
Slope-intercept form \(y=mx+b\) gives the slope \(m\) and the \(y\)-intercept \(b\) directly.
Plot \(b\) first, then use the slope's rise over run to find more points.
Graphing from slope and intercept.
Reading \(y=mx+b\).
The form:
\[y=mx+b\]
Slope is rise over run.
How to graph a line
- Plot the \(y\)-intercept \((0,b)\).
- From there, rise and run by the slope.
- Plot a second point.
- Draw the line through them.
Example 1 — Identify m and b
In \(y=2x+1\), name the slope and intercept.
Solution
Read the coefficients.
| \(m\) | \(=\) | \(2\) |
| \(b\) | \(=\) | \(1\) |
Example 2 — Plot
How do you graph \(y=2x+1\)?
Solution
Plot \((0,1)\), then rise \(2\), run \(1\).
Example 3 — Negative slope
Describe the graph of \(y=-x+4\).
Solution
Starts at \((0,4)\), falls \(1\) per step.
Example 4 — Find y
For \(y=2x+1\), find \(y\) at \(x=3\).
Solution
Substitute.
| \(y\) | \(=\) | \(2(3)+1=7\) |
Common pitfalls
\(b\) is the \(y\)-intercept, not the slope.
Slope is rise over run, not run over rise.
A negative slope falls left to right.
Frequently asked questions
What is slope-intercept form?
\(y=mx+b\).
What does b represent?
The \(y\)-intercept.
What does m represent?
The slope.
How do I start graphing?
Plot the \(y\)-intercept.
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Linear vs. non-linear functions
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Modelling linear relationships (rate of change and initial value)
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