Algebra
Linear functions
x- and y-intercepts
20 practice questions
2 video lessons
Theory + worked examples
Theory
The intercepts are where a line crosses the axes:
- \(x\)-intercept: set \(y=0\) and solve — the point \((x,0)\).
- \(y\)-intercept: set \(x=0\) — the point \((0,y)\).
Two points determine a line, so the intercepts are enough to graph it.
\(x\)-intercept on the \(x\)-axis, \(y\)-intercept on the \(y\).
Finding the intercepts.
Finding intercepts:
\[\text{x-int: } y=0,\qquad \text{y-int: } x=0\]
The \(y\)-intercept is the \(b\) in \(y=mx+b\).
How to find intercepts
- Set \(y=0\); solve for the \(x\)-intercept.
- Set \(x=0\); read the \(y\)-intercept.
- Plot both points.
- Draw the line through them.
Example 1 — x-intercept
Find the \(x\)-intercept of \(y=-1.5x+3\).
Solution
Set \(y=0\).
| \(0\) | \(=\) | \(-1.5x+3\) |
| \(x\) | \(=\) | \(2\) |
Example 2 — y-intercept
Find the \(y\)-intercept of \(y=-1.5x+3\).
Solution
Set \(x=0\).
| \(y\) | \(=\) | \(3\) |
Example 3 — From standard form
Find both intercepts of \(4x-2y=8\).
Solution
Set each variable to zero.
| \(y=0\) | \(\Rightarrow\) | \(x=2\) |
| \(x=0\) | \(\Rightarrow\) | \(y=-4\) |
Example 4 — Graph from intercepts
How can two intercepts help you graph a line?
Solution
Plot both intercepts and draw the line through them — two points determine a line.
Common pitfalls
\(x\)-intercept uses \(y=0\) — don't swap them.
The \(y\)-intercept is \(b\) in slope-intercept form.
An intercept is a point, not just a number.
Frequently asked questions
What is the x-intercept?
Where the line crosses the \(x\)-axis (\(y=0\)).
What is the y-intercept?
Where the line crosses the \(y\)-axis (\(x=0\)).
How do you find the x-intercept?
Set \(y=0\) and solve for \(x\).
Why are intercepts useful for graphing?
Two points determine a line.
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