A parking garage charges $5.50 to park for 4 hours and $7.75 to park for 7 hours. If the cost is a linear function of a number of hours parked, what is the cost to park for 3 hours?

Question

A parking garage charges $5.50 to park for 4 hours and $7.75 to park for 7 hours. If the cost is a linear function of a number of hours parked,  what is the cost to park for 3 hours?

whpalmer4 · Answer

If the cost is a linear function, it can be expressed as the equation of a line in slope-intercept form:

$$y=mx+b$$where $m$, the slope of the line, is the cost per hour, and $b$, the $y$-intercept of the line, is the charge to go into the garage and immediately leave.

You have a line that passes through the points $(4,5.50)$ and $(7,7.75)$.  Can you work out the slope and $y$-intercept knowing that?  That will give you the equation to find the cost for parking for an arbitrary length of time.