Algebra
Linear functions
Slope-intercept form
20 practice questions
2 video lessons
Theory + worked examples
Theory
Slope-intercept form is
\[y=mx+b,\]
where \(m\) is the slope and \(b\) is the \(y\)-intercept.
Read \(m\) and \(b\) straight off the equation to graph or interpret.
\(y=2x-3\): slope \(2\), \(y\)-intercept \(-3\).
Reading slope-intercept form.
Slope-intercept form:
\[y=mx+b\]
Start at \(b\), then step by \(m\) to graph.
How to use slope-intercept form
- Identify \(m\) (coefficient of \(x\)) and \(b\) (constant).
- Plot the \(y\)-intercept \(b\).
- Step by the slope \(m\).
- Convert from other forms by solving for \(y\).
Example 1 — Identify m and b
Give the slope and \(y\)-intercept of \(y=2x-3\).
Solution
Read the coefficients.
| \(m\) | \(=\) | \(2\) |
| \(b\) | \(=\) | \(-3\) |
Example 2 — From a graph
A line has \(y\)-intercept \(1\) and slope \(\dfrac12\). Write it.
Solution
Substitute into \(y=mx+b\).
| \(y\) | \(=\) | \(\dfrac12 x+1\) |
Example 3 — Convert
Write \(2x+y=5\) in slope-intercept form.
Solution
Solve for \(y\).
| \(y\) | \(=\) | \(-2x+5\) |
Example 4 — Interpret b
In \(C=15h+40\), what is \(b\) and what does it mean?
Solution
\(b=40\), the starting value (a fixed fee).
Common pitfalls
\(b\) is the \(y\)-intercept, the value at \(x=0\).
Solve for \(y\) before reading \(m\) and \(b\).
\(m\) is the coefficient of \(x\), not the constant.
Frequently asked questions
What is slope-intercept form?
\(y=mx+b\), showing slope and \(y\)-intercept.
What is \(m\)?
The slope.
What is \(b\)?
The \(y\)-intercept, the value at \(x=0\).
How do you graph from this form?
Plot \(b\), then step by the slope \(m\).
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