Question

The rate of change between two points is 3. If the two points are (3.5) and (8,m).

what is the value of m? Explain how you determined your answer

Answer 1

`m = 20`

Explanation:

Given

Points (3.5) and (8,m)

Rate of change = 3

Required

Find m

Basically, rate of change means slope or gradient;

So, we'll apply the formula of slope/gradient to solve for m;

Slope is calculated as thus;

`Slope = (y_2 -y_1)/(x_2 - x_1)`

Where

`(x_1,y_1) = (3,5); (x_2,y_2) = (8,m);`

So;

`Slope = (y_2 -y_1)/(x_2 - x_1)` becomes

`Slope = (m - 5)/(8-3)`

Recall that rate of change = 3;

Substitute 3 for slope

`3 = (m - 5)/(8-3)`

`3 = (m - 5)/(5)`

Multiply both sided by 5

`5 * 3 = (m - 5)/(5) * 5`

`15 = m - 5}`

Add 5 to both sides

`5 + 15 = m - 5 + 5`

`20 = m`

`m = 20`