Question

1. trish is ordering travel mugs from a website that charges a certain amount per mug plus a flat rate for shipping as shown in the table.

a. write an equation to represent the situation.
b. what does the y - intercept mean in the context of the situation?
c. what does the slope mean in the context of the situation?

Explanation:

Step1: Find the slope

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,5.99)\) and \((x_2,y_2)=(3,32.24)\). Then \(m=\frac{32.24 - 5.99}{3-0}=\frac{26.25}{3}=8.75\). The equation of a line in slope - intercept form is \(y = mx + b\), where \(b\) is the \(y\) - intercept. When \(x = 0\), \(y=b\), so \(b = 5.99\). The equation is \(y=8.75x + 5.99\).

Step2: Interpret the \(y\) - intercept

The \(y\) - intercept (\(x = 0\)) represents the flat rate for shipping. When \(x = 0\) (no mugs are ordered), the cost \(y\) is the flat - rate shipping cost. So the flat - rate shipping cost is \(\$5.99\).

Step3: Interpret the slope

The slope \(m = 8.75\) represents the cost per mug. For each additional mug (\(\Delta x=1\)), the cost (\(y\)) increases by \(\$8.75\).

Answer:

a. The equation is \(y = 8.75x+5.99\).
b. The \(y\) - intercept (\(5.99\)) means the flat - rate shipping cost.
c. The slope (\(8.75\)) means the cost per mug.