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 lines slope. check the result by using the coefficient of x in the lines equation.
$y = \frac{1}{8}x - 4$

a. b. c. d.
(the graphs are shown in $ - 10,10,2$ by $ - 10,10,2$ viewing rectangles.)
two points on the graph are $(-1,\square)$ and $(3,\square)$
(type integers or decimals.)

Explanation:

Step1: Find y at x=-1

Substitute $x=-1$ into $y=\frac{1}{8}x - 4$:
$y=\frac{1}{8}(-1) - 4 = -\frac{1}{8} - 4 = -0.125 - 4 = -4.125$

Step2: Find y at x=3

Substitute $x=3$ into $y=\frac{1}{8}x - 4$:
$y=\frac{1}{8}(3) - 4 = \frac{3}{8} - 4 = 0.375 - 4 = -3.625$

Step3: Verify slope from points

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ with $(x_1,y_1)=(-1,-4.125)$ and $(x_2,y_2)=(3,-3.625)$:
$m=\frac{-3.625 - (-4.125)}{3 - (-1)}=\frac{0.5}{4}=\frac{1}{8}$

Step4: Match to correct graph

The line has a positive slope $\frac{1}{8}$ and y-intercept $-4$, so it rises gently from left to right and crosses the y-axis at $(0,-4)$. This matches option C.

Answer:

Correct graph: C.
Two points: $(-1, -4.125)$ and $(3, -3.625)$
Slope verification: The calculated slope $\frac{1}{8}$ matches the coefficient of $x$ in the equation.