Question

1. fara wants to rent a tent for an outdoor celebration. the cost of the tent is $500 per hour, plus an additional $100 set - up fee.

a. draw a line to show the relationship between the number of hours the tent is rented, x, and the total cost of the tent, y.
b. what is the equation of the line in slope - intercept form?

Explanation:

Part a:

Step 1: Identify the equation

The total cost \( y \) is the set - up fee plus the cost per hour times the number of hours. The set - up fee is $100 and the cost per hour is $500. So the equation is \( y = 500x+100 \).

Step 2: Find two points on the line

• When \( x = 0 \) (0 hours rented), \( y=500(0)+100 = 100 \). So the point is \( (0,100) \).
• When \( x = 1 \) (1 hour rented), \( y = 500(1)+100=600 \). So the point is \( (1,600) \).

Step 3: Plot the points and draw the line

Plot the points \( (0,100) \) and \( (1,600) \) on the given coordinate plane (where the x - axis is hours and y - axis is cost in dollars) and draw a straight line through them.

Part b:

Step 1: Recall the slope - intercept form

The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value).

Step 2: Determine \( m \) and \( b \)

• The cost per hour is $500, which is the rate of change. So \( m = 500 \).
• The set - up fee of $100 is the initial cost (when \( x = 0 \)), so \( b = 100 \).

Step 3: Write the equation

Substitute \( m = 500 \) and \( b = 100 \) into the slope - intercept form \( y=mx + b \). We get \( y = 500x+100 \).

Answer:

(for part b):
The equation of the line in slope - intercept form is \( y = 500x+100 \)