Question

A parking garage is located in the downtown area of a city. The

table below shows the cost for parking in the garage for different
amounts of time.
Hours Parked
Cost of Parking
1
$8.80 1 1/2 $10.70
4
$20.20
5
$24
7 1/2
$33.50
10
$43
a) What equation represents the cost of parking in the garage,
y, for x hours?
b) Sketch a graph to represent the cost of parking over time.

Answer 1

a) y = 3.80x +5.00

b) see attached

Explanation:

A graph shows the given table values lie on a straight line.

__

a)

Finding the slope of the line is made easier by an appropriate choice of a pair of table values:

m = (y2 -y1)/(x2 -x1)

m = (24 -20.20)/(5 -4) = 3.80/1 = 3.80 . . . . using (4, 20.20) and (5, 24)

The y-intercept can likewise be found with an appropriate choice of table values. Solving the slope-intercept equation for b, we get ...

y = mx +b

b = y -mx

b = 8.80 -3.80 × 1 = 5.00 . . . . using the first table value

An equation that represents the cost of parking could be ...

y = 3.80x +5.00

__

b)

A graph of the table values and the equation is shown in the attachment.