Question

1. the table & graph show the hourly charges for two parking garages.

a identify the slope and y - intercept for each garage.
garage a -> slope:
equation:
garage b -> slope:
equation:
show all your work below for finding the slope & intercept
b what does the slope represent for each garage?
c what does the y - intercept represent for each garage?
d. garage _ has a greater rate of change. garage _ has a greater initial value.
e if you wanted to park your car for 12 hours, how much would it cost for each garage? which would cost less?
garage a:
garage b:

(table for garage a:
time (h): 0, 1, 2, 3, 4
charge ($): 5, 7, 9, 11, 13

graph for garage b:
time (h) on x - axis (0 - 6), charge ($) on y - axis (0 - 12), with plotted points)

Explanation:

Step1: Find Garage A slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$. Use $(0,5)$ & $(1,7)$:
$m=\frac{7-5}{1-0}=2$

Step2: Find Garage A y-intercept

Y-intercept is $y$ when $x=0$: from table, $b=5$

Step3: Garage A equation

Slope-intercept form: $y=mx+b$
$y=2x+5$

Step4: Find Garage B slope

Use graph points $(0,6)$ & $(1,7)$:
$m=\frac{7-6}{1-0}=1$

Step5: Find Garage B y-intercept

Y-intercept is $y$ when $x=0$: from graph, $b=6$

Step6: Garage B equation

Slope-intercept form: $y=mx+b$
$y=x+6$

Step7: Interpret slope/ y-intercept

Slope = hourly parking rate; y-intercept = initial fee

Step8: Compare rate/initial value

Garage A slope (2) > Garage B slope (1); Garage B y-intercept (6) > Garage A y-intercept (5)

Step9: Calculate 12-hour cost Garage A

Substitute $x=12$ into $y=2x+5$:
$y=2(12)+5=24+5=29$

Step10: Calculate 12-hour cost Garage B

Substitute $x=12$ into $y=x+6$:
$y=12+6=18$

Step11: Compare 12-hour costs

$18 < 29$, so Garage B is cheaper

Answer:

A.
Garage A -> Slope: $2$, y-intercept: $5$, Equation: $y=2x+5$
Garage B -> Slope: $1$, y-intercept: $6$, Equation: $y=x+6$
B.
For Garage A: The slope represents the $2 hourly parking charge.
For Garage B: The slope represents the $1 hourly parking charge.
C.
For Garage A: The y-intercept represents the $5 initial parking fee.
For Garage B: The y-intercept represents the $6 initial parking fee.
D.
Garage A has a greater rate of change. Garage B has a greater initial value.
E.
Garage A: $29; Garage B: $18. Garage B would cost less.