Question

1. relationship a is defined by the equation: y=5x some values of relationship b are shown in the table. relationship b x y 0 0 3 12.3 5 20.5 both relationships represent a direct proportion between x and y. the rate of change in relationship a is how many units greater than the rate of change in relationship b?

Explanation:

Step1: Find rate of change for A

The equation for Relationship A is \( y = 5x \). For a direct proportion \( y = kx \), the rate of change (slope) \( k \) is 5. So rate of change for A is 5.

Step2: Find rate of change for B

For Relationship B, use two points \((0,0)\) and \((3,12.3)\) (or \((5,20.5)\)). The rate of change (slope) \( k \) is calculated as \( \frac{y_2 - y_1}{x_2 - x_1} \). Using \((0,0)\) and \((3,12.3)\): \( \frac{12.3 - 0}{3 - 0} = \frac{12.3}{3} = 4.1 \). Let's verify with \((0,0)\) and \((5,20.5)\): \( \frac{20.5 - 0}{5 - 0} = \frac{20.5}{5} = 4.1 \). So rate of change for B is 4.1.

Step3: Find the difference

Subtract the rate of change of B from A: \( 5 - 4.1 = 0.9 \).

Answer:

0.9