X-Intercept
In short: An x-intercept of a graph is a point lying right on the horizontal axis, so its height is zero and it is written (a, 0).
Algebra 1Functions and GraphsF-IF.B.4
What is X-Intercept?
Wherever a line or curve meets the horizontal axis, you have located its x-intercept. Heights along that axis are all zero, which is why the point always has the form \((a, 0)\).
From an equation, substitute 0 for y (or for \(f(x)\)) and solve what remains for x. In a story problem, the point often marks the moment something runs out, lands or breaks even. A graph may have one such point, none at all, or several.
How to spot it
- The question asks where the picture meets the horizontal axis, or where the height becomes zero.
- Wording such as runs out, breaks even or hits the ground points to a zero output.
- You are asked for the zeros, roots or solutions of an equation set equal to 0.
- An equation is in standard form and you want two quick points to graph it.
The method
- Write the equation and replace y or \(f(x)\) with 0.
- Solve the resulting equation for x, factoring or using inverse operations as needed.
- Write each answer as a point \((a, 0)\), keeping the zero as the y-coordinate.
- Check by substituting the x-value back into the original equation to get 0.
X-Intercept: solved example
Problem
A hot air balloon over New Mexico descends so that its altitude in feet after t minutes is \(A(t) = 1{,}260 – 45t\). When does the balloon touch the ground?
Solution
Landing means the altitude is zero, so find the x-intercept: \(1{,}260 – 45t = 0\).
Add \(45t\) to both sides: \(1{,}260 = 45t\). Divide by 45: \(t = 28\). The intercept is \((28, 0)\), so the balloon lands after 28 minutes.
Try it
Question 1
Find the x-intercept of \(3x – 2y = 18\).
Show the answer
Set \(y = 0\): \(3x = 18\), so \(x = 6\). The intercept is \((6, 0)\).
Question 2
Find the x-intercepts of \(y = x^2 – 16\).
Show the answer
Solve \(x^2 – 16 = 0\): \(x = 4\) or \(x = -4\). The points are \((4, 0)\) and \((-4, 0)\).
X-Intercept vs. Y-Intercept
The pair work as mirror images. This one sits on the horizontal axis and comes from making y zero. The y-intercept sits on the vertical axis and comes from making x zero. Zeroing the wrong letter is the classic slip, so jot “y = 0” before solving.
Keep going
Lessons
Worksheets and quizzes
Related words
- Y-Intercept
- Zeros of a Function
- Standard Form of a Linear Equation
- Linear Equation
- Slope-Intercept Form
- Coordinate Plane
Whole dictionary: A–Z · Algebra 1 · Functions and Graphs