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 the number of hours parked, what is the cost to park for 3 hours?
A) $2.25
B) $2.50
C) $3.25
D) $4.75

Answer 1

Y=mx+b
m=slope
b=yint

two points
cost=y
(4,5.5) and (7,7.75)
slope=(y2-y1)/(x2-x1)
slope=(7.75-5.5)/(7-4)=2.25/3=0.75

y=0.75x+b
find b
(4,5.5)
x=4
y=5.5
5.5=0.75(4)+b
5.5=3+b
minus 3 fromboth sides
2.5=b

y=0.75x+2.5
3 hours
y=0.75(3)+2.5
y=2.25+2.5
y=4.75

answer is D

Answer 2

Slope = (7.75 - 5.50)/(7 - 4) = 2.25/3 = 0.75
The equation described by the function is
y - 5.5 = 0.75(x - 4)
y = 0.75x - 3 + 5.5 = 0.75x + 2.5
For x = 3, y = 0.75(3) + 2.5 = 2.25 + 2.5 = 4.75
Therefore, it costs $4.75 to park for 3 hours.