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.
$y = \frac{1}{8}x - 4$
(the graphs are shown in $-10,10,2$ by $-10,10,2$ viewing rectangles.)
two points on the graph are $(-1, -4.125)$ and $(3, -3.625)$.
(type integers or decimals.)
the lines slope is \\(\square\\). (type an integer or a decimal.)

Explanation:

Step1: Recall slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.

Step2: Substitute given points

Let $(x_1,y_1)=(-1,-4.125)$ and $(x_2,y_2)=(3,-3.625)$.
$m=\frac{-3.625 - (-4.125)}{3 - (-1)}$

Step3: Simplify numerator and denominator

Numerator: $-3.625 + 4.125 = 0.5$
Denominator: $3 + 1 = 4$
$m=\frac{0.5}{4}$

Step4: Calculate final slope

$m=0.125$ (or $\frac{1}{8}$, which matches the coefficient of $x$ in the given equation)

Answer:

0.125