The \(x\)-intercept occurs when \(y=0\).

And the \(y\)-intercept occurs when \(x=0\).

Practice Questions

Find the x and y intercepts for each of the following.

\(\textbf{1)}\) \(y=2x+4\)

Show x- and y- intercepts

x-intercept \((-2,0), \enspace\) y-intercept \((0,4)\)

\(\textbf{2)}\) \(2x+4y=8\)

Show x- and y- intercepts

x-intercept \((4,0), \enspace\) y-intercept \((0,2)\)

\(\textbf{3)}\) \(y=-3x+7\)

Show x- and y- intercepts

x-intercept \((\frac{7}{3},0), \enspace\) y-intercept \((0,7)\)

\(\textbf{4)}\) \(y=\frac{1}{2}x+1\)

Show x- and y- intercepts

x-intercept \((-2,0), \enspace\) y-intercept \((0,1)\)

\(\textbf{5)}\) \(y=-5x+3\)

Show x- and y- intercepts

x-intercept \((\frac{3}{5},0), \enspace\) y-intercept \((0,3)\)

\(\textbf{6)}\) \(y=x+6\)

Show x- and y- intercepts

x-intercept \((-6,0), \enspace\) y-intercept \((0,6)\)

\(\textbf{7)}\) \({\begin{array}{|c|c|c|c|c|c|}
\hline
\textbf{x} & 0 & 1 & 2 & 3 & 4 \\
\hline
\textbf{y} & 8 & 6 & 4 & 2 & 0 \\
\hline
\end{array} }
\)

Show x- and y- intercepts

x-intercept \((4,0), \enspace\) y-intercept \((0,8)\)

\(\textbf{8)}\) \({\begin{array}{|c|c|c|c|c|c|}
\hline
\textbf{x} & -1 & 0 & 1 & 2 & 3 \\
\hline
\textbf{y} & 0 & 4 & 6 & 4 & 0 \\
\hline
\end{array} }
\)

Show x- and y- intercepts

x-intercepts \((-1,0) \text{ and } (3,0), \enspace\) y-intercept \((0,4)\)

Challenge Problem

\(\textbf{9)}\) \(y=x^2-4\)

Show x- and y- intercepts

x-intercepts \((-2,0) \text{ and } (2,0), \enspace\) y-intercept \((0,-4)\)

See Related Pages\(\)

\(\bullet\text{ Graphing Linear Equations}\)
\(\,\,\,\,\,\,\,\,2x-3y=6 \)

\(\bullet\text{ Slope Formula}\)
\(\,\,\,\,\,\,\,\,m=\frac{y_2-y_1}{x_2-x_1}\)

\(\bullet\text{ Net Change}\)
\(\,\,\,\,\,\,\,\,y_2-y_1\)

\(\bullet\text{ Slope Intercept Form}\)
\(\,\,\,\,\,\,\,\,y=mx+b\)

\(\bullet\text{ Point Slope Form}\)
\(\,\,\,\,\,\,\,\,y-y_1=m(x-x_1)\)

\(\bullet\text{ Parallel and Perpendicular Slope}\)
\(\,\,\,\,\,\,\,\,m_1=m+2,\,\,\,m_1=\frac{1}{m_2}\)

\(\bullet\text{ Distance Between a Point and a Line}\)
\(\,\,\,\,\,\,\,\,(3,4) \text{ and } y=\frac{3}{4}x−2\)

\(\bullet\text{Finding x- and y- intercepts}\)
\(\,\,\,\,\,\,\,\,y=2x+4\)

\(\bullet\text{ Andymath Homepage}\)

In Summary

Finding the x and y intercepts of a graph involves determining the points where the graph crosses the x and y axes. If you have a graph, you can look on the graph. If you are given an equation, you can plug in x=0 to find the y-intercept and plug in y=0 to find the x-intercept. This is easiest with standard form \(Ax+By=C\), but works for any linear equation in any form.

This is typically first learned in algebra and pre-calculus classes.

About Andymath.com

Andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. If you have any requests for additional content, please contact Andy at tutoring@andymath.com. He will promptly add the content.

Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. In the future, I hope to add Physics and Linear Algebra content.

Visit me on Youtube, Tiktok, Instagram and Facebook. Andymath content has a unique approach to presenting mathematics. The clear explanations, strong visuals mixed with dry humor regularly get millions of views. We are open to collaborations of all types, please contact Andy at tutoring@andymath.com for all enquiries. To offer financial support, visit my Patreon page. Let’s help students understand the math way of thinking!

Thank you for visiting. How exciting!