Question

Can someone help me with these problems? Please!

Answer 1

Explanation:

2) Slope can be written as rise over run:

• rise: add to the y-value
• run: add to the x-value

`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)`

3) Slope formula is:
`(y_2-y_1)/(x_2-x_1)`

`slope=(15-3)/(5-1)=(12)/(4)=\boxed{3}`

4) Average rate of change is the slope of the given interval:

a) when x = 0, y = 0 and when x = 1, y = -3

`Slope=(-3-0)/(1-0)=(-3)/(1)=-3`

b) when x = -2, y = 0 and when x = -1, y = 3

`Slope=(3-0)/(-1+2)=(3)/(1)=3`

c) when x = 0, y = 0 and when x = 2, y = 0

`Slope=(0-0)/(2-0)=(0)/(2)=0`