Answer:
B) The slope of [tex]f(x)[/tex] is same as the slope of [tex]g(x)[/tex]
Step-by-step explanation:
Given function:
[tex]g(x)=-3x-6[/tex]
Comparing the function with slope intercept equation of line i.e.
[tex]y=mx+b[/tex]
where [tex]m[/tex] represents slope and [tex]b[/tex] represents y-intercept.
So, we can find [tex]m[/tex] for [tex]g(x)[/tex] which is the co-efficient of the [tex]x[/tex] term.
Slope of [tex]g(x)=-3[/tex]
From graph of [tex]f(x)[/tex] we have two points on the line which are:
[tex](0,2)[/tex] and [tex](-1,5)[/tex]
Slope of line can be given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{5-2}{-1-0}[/tex]
[tex]m=\frac{3}{-1}[/tex]
∴ [tex]m=-3[/tex]
So, we find that slope of [tex]f(x)[/tex] is same as [tex]g(x)[/tex]
