Answer: OPTION B.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Given:
[tex]f(x)=-2x+3[/tex]
You can identify that its slope is:
[tex]m=-2[/tex]
By definition, the slope can be calculated with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Then, in order to find the slope of g(x), you can pick the points (2,-8) and (6,4) and say that:
[tex]y_2=-8\\y_1=4\\\\x_2=2\\x_1=6[/tex]
So, substituting these values into the formula, you get:
[tex]m=\frac{-8-4}{2-6}=3[/tex]
If you subtract the slopes, you get that the positive difference between them, is:
[tex]3-(-2)=5[/tex]
