Question

A truck driver earns a daily amount based on the number of miles he drives on Monday here and $70 for driving 120 miles and on Tuesday he earns $102.50 for driving to 50 miles explain how to derive A linear function that expresses the daily amount she earns fir driving X miles that day show your work and intercept the rate of change and initial value of the function.

Answer 1

Let x represent miles and y represent dollars.
That gives you coordinates (120, 70) and (50, 102.5).
First, find the slope (m) of the line using $\frac{y_{2} - y_{1} }{ x_{2} - x_{1}}$
m = $\frac{70 - 102.5}{120 - 50}$
    = $\frac{-32.5}{70}$ = $\frac{-65}{140} = \frac{-13}{28}$
Note: slope is rate of change.

Next, use the Point-Slope formula and solve for y:
y - $y_{1}$ = m (x - $x_{1}$)
y - 70 = $\frac{-13}{28}$(x - 120)
y - 70 = $\frac{-13}{28}$x + $\frac{390}{7}$
      y  = $\frac{-13}{28}$x + $\frac{880}{7}$

Answer:
linear function is: y  = $\frac{-13}{28}$x + $\frac{880}{7}$
rate of change is: $\frac{-13}{28}$
initial value of the function: $\frac{880}{7}$