Chapter 3, Problem 24CR

To determine

To find: slope, y-intercept, and x-intercept of the graph.

Answer to Problem 24CR

Slope $m=-\frac{2}{3}$

The x-intercept is 3.

Explanation of Solution

Given information: A linear function h models a relationship in which the dependent variable decreases 2 units for every 3 units the independence variable increases. And $h\left(0\right)=2$ .

Formula used:

  $h\left(x\right)=mx+c$

Where $m$ is the slope and $c$ is the constant,

  $\text{Slope=}\frac{\text{independent}\text{variable}}{\text{dependent variable}}$

Calculation:

The function $h$ is linear function,

And the y-intercept $h\left(0\right)=2$ ,

  $\begin{array}{l}h\left(0\right)=m\left(0\right)+c\\ 2=c\end{array}$

The dependent variable decreases 2 units for every 3 units the independent variable increases,

Therefore,

  $\begin{array}{l}\text{Slope=}\frac{\text{independent}\text{variable}}{\text{dependent variable}}\\ m=-\frac{2}{3}\end{array}$

Substitute slope in slope intercept form of the equation,

  $\begin{array}{l}y=mx+c\\ 0=-\frac{2}{3}x+2\\ \frac{2}{3}x=2\\ x=3\end{array}$

Therefore the x-intercept is 3.