Question

Bob parked his car at the local garage. If his car stayed for one hour, he would have been charged $6.00. If he stayed for 4 hours, he would have been charged $16.50. How can we use this information to find the equation that represents both the initial charge as well as the hourly charge? Please describe what you would do. SOLVE if possible

Answer 1

Initial charge is $2.5

Hourly charge is $3.5/hr

Equation is y=3.5x+2.5

Explanation:

Getting slope

Get fixed charge

Get equation

The slope can be found as follows. For 1 hour, charges is $6 so making time in x axis while money charged in y axis, the first coordinate is (1, 6) while for 4 hours with charge of $16.5 the coordinate will be (4, 16.5)

The slope will be given by dividing change in y axis to change in x axis. This will be (16.5-6)/(4-1)=3.5

To get the fixed charge

Using the equation y=mx+c where m is slope while c is fixed charge, x is time and y is total cost then for 1 hour

6=3.5(1)+c

C=6-3.5=2.5

Therefore, generally the equation will be y=3.5x+2.5

Initial charge is $2.5

Hourly charge is $3.5/hr

Equation is y=3.5x+2.5