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 \((0,4)\)

Show Work

\(\textbf{x-intercept:}\)
\(\,\,\,\,\,\,y = 0\)
\(\,\,\,\,\,\,0 = 2x + 4\)
\(\,\,\,\,\,\,2x = -4\)
\(\,\,\,\,\,\,x = -2\)
x-intercept: \((-2, 0)\)
\(\textbf{y-intercept:}\)
\(\,\,\,\,\,\,x = 0\)
\(\,\,\,\,\,\,y = 2(0) + 4\)
\(\,\,\,\,\,\,y = 4\)
y-intercept: \((0, 4)\)

 

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

Show x- and y- intercepts

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

Show Work

\(\textbf{x-intercept:}\)
\(\,\,\,\,\,\,y = 0\)
\(\,\,\,\,\,\,2x + 4(0) = 8\)
\(\,\,\,\,\,\,2x = 8\)
\(\,\,\,\,\,\,x = 4\)
x-intercept: \((4, 0)\)
\(\textbf{y-intercept:}\)
\(\,\,\,\,\,\,x = 0\)
\(\,\,\,\,\,\,2(0) + 4y = 8\)
\(\,\,\,\,\,\,4y = 8\)
\(\,\,\,\,\,\,y = 2\)
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.