Answer:
[tex]m = 20[/tex]
Step-by-step 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;
[tex]Slope = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (3,5); (x_2,y_2) = (8,m);[/tex]
So;
[tex]Slope = \frac{y_2 -y_1}{x_2 - x_1}[/tex] becomes
[tex]Slope = \frac{m - 5}{8-3}[/tex]
Recall that rate of change = 3;
Substitute 3 for slope
[tex]3 = \frac{m - 5}{8-3}[/tex]
[tex]3 = \frac{m - 5}{5}[/tex]
Multiply both sided by 5
[tex]5 * 3 = \frac{m - 5}{5} * 5[/tex]
[tex]15 = m - 5}[/tex]
Add 5 to both sides
[tex]5 + 15 = m - 5 + 5[/tex]
[tex]20 = m[/tex]
[tex]m = 20[/tex]
