Example 5
Completion requirements
| Example 5 |
Algebraically determine the \(x\)- and \(y\)-intercepts of the linear function \(y = -\frac{1}{4}x + 5\), and then use the results to graph the function.
Graph (using the intercepts)
To graph the function, plot the two intercepts. Because the function is linear, you can draw a straight line connecting the points to complete the graph. Be sure to label the function and points on the graph.
\(x\)-intercept \((y = 0)\)
\(\begin{align}
y &= -\frac{1}{4}x + 5 \\
0 &= -\frac{1}{4}x + 5 \\
-5 &= -\frac{1}{4}x \\
20 &= x \\
\end{align}\)
\((20, 0)\)
The \(x\)-intercept is 20.
\(\begin{align}
y &= -\frac{1}{4}x + 5 \\
0 &= -\frac{1}{4}x + 5 \\
-5 &= -\frac{1}{4}x \\
20 &= x \\
\end{align}\)
\((20, 0)\)
The \(x\)-intercept is 20.
\(y\)-intercept \((x = 0)\)
\(\begin{align}
y &= -\frac{1}{4}x + 5 \\
y &= -\frac{1}{4}\left( 0 \right) + 5 \\
y &= 5 \\
\end{align}\)
\((0, 5)\)
The \(y\)-intercept is 5.
\(\begin{align}
y &= -\frac{1}{4}x + 5 \\
y &= -\frac{1}{4}\left( 0 \right) + 5 \\
y &= 5 \\
\end{align}\)
\((0, 5)\)
The \(y\)-intercept is 5.
Graph (using the intercepts)
To graph the function, plot the two intercepts. Because the function is linear, you can draw a straight line connecting the points to complete the graph. Be sure to label the function and points on the graph.