Step-by-step explanation:
2) Slope can be written as rise over run:
- rise: add to the y-value
- run: add to the x-value
[tex]a) Slope=-1\ over\ 1\quad \rightarrow \quad (11 + 1, -8 - 1)\implies (12, -9)\\b) Slope=7\ over\ 2\quad \rightarrow \quad (2+2,2+7)\implies (4, 9)\\c) Slope=9\ over\ 4\quad \rightarrow \quad (-5+4,-2+9)\implies (-1, 7)[/tex]
3) Slope formula is: [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]slope=\dfrac{15-3}{5-1}=\dfrac{12}{4}=\boxed{3}[/tex]
4) Average rate of change is the slope of the given interval:
a) when x = 0, y = 0 and when x = 1, y = -3
[tex]Slope=\dfrac{-3-0}{1-0}=\dfrac{-3}{1}=-3[/tex]
b) when x = -2, y = 0 and when x = -1, y = 3
[tex]Slope=\dfrac{3-0}{-1+2}=\dfrac{3}{1}=3[/tex]
c) when x = 0, y = 0 and when x = 2, y = 0
[tex]Slope=\dfrac{0-0}{2-0}=\dfrac{0}{2}=0[/tex]
