Question

Find the rate of change between

(-1,-4)
(3,1)

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.

`(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{1 +4}{3 +1} \implies {\Large \begin{array}{llll} \cfrac{ 5 }{ 4 } \end{array}}`

Answer 2

Slope formula -
`(y2-)/(x2-) (y1)/(x1)`

First coordinate pair - (-1, -4)

Second coordinate pair - (3, 1)

Coordinate format - (x, y)

y2=1, y1=-4

x2=3, x1=-1

`(1-)/(3-) ((-4))/((-1)) =(5)/(4)`

Hope this is what your looking for :)