Question

carla hands out flyers for a band concert. the graph shows the number of flyers she hands out, y, as a function of the time, in minutes, x. use the graph to describe the function. the initial value is 0. it represents the number of flyers carla hands out in 0 minutes. the number of flyers carla hands out increases over time. that means the rate of change is positive. the rate of change represents the number of flyers carla? the rate of change is?.

Explanation:

Step1: Find the rate of change formula

The rate of change (slope) formula for a linear function \(y = mx + b\) (where \(m\) is the slope) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\). In this case, the line passes through \((0,0)\) and \((4,20)\).

Step2: Calculate the rate of change

Substitute \(x_1 = 0,y_1=0,x_2 = 4,y_2 = 20\) into the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

$$m=\frac{20 - 0}{4 - 0}=\frac{20}{4}=5$$

The rate of change represents the number of flyers Carla hands out per minute.

Answer:

The rate of change represents the number of flyers Carla hands out per minute. The rate of change is \(5\).