Question

use a graphing utility to graph the equation below. then use the trace feature to trace along the line and find the coordinates of two points. use these points to compute the line’s slope. check the result by using the coefficient of x in the line’s equation.
$y = \frac{1}{8}x - 4$

choose the correct graph below
a. b. c. d
(the graphs are shown in $-10,10,2$ by $-10,10,2$ viewing rectangles.)

Explanation:

Step1: Identify line parameters

The equation is $y = \frac{1}{8}x - 4$. This is in slope-intercept form $y=mx+b$, where slope $m=\frac{1}{8}$ (positive, shallow slope) and y-intercept $b=-4$ (line crosses y-axis at $(0,-4)$).

Step2: Verify points on the line

• When $x=0$, $y = \frac{1}{8}(0)-4 = -4$, so point $(0,-4)$ is on the line.
• When $x=8$, $y = \frac{1}{8}(8)-4 = 1-4=-3$, so point $(8,-3)$ is on the line.

Step3: Calculate slope from points

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(0,-4)$ and $(x_2,y_2)=(8,-3)$:
$\frac{-3 - (-4)}{8 - 0} = \frac{1}{8}$
This matches the coefficient of $x$ in the equation.

Step4: Match to correct graph

The line has a shallow positive slope and crosses the y-axis at $y=-4$, which falls in the $[-10,10,2]$ viewing rectangle. The correct graph will show a line rising slowly from left to right, passing near $(0,-4)$ and $(8,-3)$.

Answer:

(Select the graph with a shallow positive-sloped line crossing the y-axis at $y=-4$; based on the parameters, this corresponds to the option that visually matches the line $y=\frac{1}{8}x-4$ in the given viewing window. Additionally, the calculated slope is $\frac{1}{8}$, which confirms the coefficient of $x$ in the original equation is correct.)