Question

I need help with this question

Answer 1

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{27}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{27}-\stackrel{y1}{9}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{ 18 }{ 4 } \implies \cfrac{9}{2}`

Answer 2

rate of change = 4.5

Explanation:

rate of change in the graph is defined as the slope and is demonstrated by the formula:

rate of change = change in y / change in x

= y2 - y1 / x2 - x1

let's take any two co-ordinates from the graph given:

x1, y1 = 2, 9

x2, y2 = 4, 18

rate of change = 18 - 9 / 4 - 2

= 9/2 = 4.5