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
`(y_(2) - y_(1) )/( x_(2) - x_(1))`
m =
`(70 - 102.5)/(120 - 50)`
=
`(-32.5)/(70)` =
`(-65)/(140) = (-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 =
`(-13)/(28)`(x - 120)
y - 70 =
`(-13)/(28)`x +
`(390)/(7)`
y =
`(-13)/(28)`x +
`(880)/(7)`

Answer:
linear function is: y =
`(-13)/(28)`x +
`(880)/(7)`
rate of change is:
`(-13)/(28)`
initial value of the function:
`(880)/(7)`