Question

1 a restaurant offers delivery for their pizzas for a fee added to the price of the pizzas. one customer pays $25 to have 2 pizzas delivered. another customer pays $58 to have 5 pizzas delivered. how many pizzas are delivered to a customer who paid $80?
2 to paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for each hour of labor.
a. how much would the painting company charge to paint a house that needs 20 hours of labor?
a house that needs 50 hours?
b. draw a line representing the relationship between x, the number of hours it takes the painting company to finish the house, and y, the total cost of painting the house. label the two points from the earlier question on your graph.
graph with x (time in hours) from 0 to 60 and y (total cost in dollars) from 0 to 4000
c. find the slope of the line. what is the meaning of the slope in this context?

Explanation:

Question 2a

Step1: Determine the cost formula

The cost formula is \(y = 50x+500\), where \(x\) is the number of hours of labor and \(y\) is the total cost.

Step2: Calculate for \(x = 20\)

Substitute \(x = 20\) into the formula: \(y=50\times20 + 500=1000 + 500=\$1500\)

Step3: Calculate for \(x = 50\)

Substitute \(x = 50\) into the formula: \(y=50\times50+500 = 2500+500=\$3000\)

Step1: Recall the slope formula

The slope formula for a line \(y=mx + b\) is \(m\). In the equation \(y = 50x+500\), the coefficient of \(x\) is the slope.

Step2: Interpret the slope

The slope \(m = 50\). In this context, it means that for each additional hour of labor, the total cost of painting the house increases by \(\$50\).

Answer:

For 20 hours of labor, the cost is \(\$1500\). For 50 hours of labor, the cost is \(\$3000\).

Question 2c