Question

number of large posters | price (dollars)
5 | 178
8 | 274
11 | 370
14 | 466
a poster company charges a set delivery fee in addition to a constant fee for every large poster ordered. the table compares the number of large posters ordered and the charges in dollars. what is the delivery fee?

Explanation:

Step1: Find the cost per poster

Let the cost per poster be \( m \) and delivery fee be \( b \). The equation is \( y = mx + b \). Using two points \((5, 178)\) and \((8, 274)\), the slope \( m=\frac{274 - 178}{8 - 5}=\frac{96}{3}=32 \).

Step2: Calculate delivery fee

Substitute \( x = 5 \), \( y = 178 \), and \( m = 32 \) into \( y=mx + b \). So, \( 178=32\times5 + b \). \( 178 = 160 + b \), then \( b=178 - 160 = 18 \).

Answer:

The delivery fee is 18 dollars.