Exercise 21 Page 158

We will use the given information to determine some features of the function, starting with the slope.

Slope

Consider what slope represents. It is a change in the $x\text{-}$ and $y\text{-}$values of the graph. We are told that the dependent variable $y$ $\text{decreases}$ by $2$ units every time the independent variable $x$ $\text{increases}$ by $3$ units.

$y\text{-}$intercept

Think of the point where the graph of an equation crosses the $y\text{-}$axis. The $x$-value of that $(x,y)$ coordinate pair is $0,$ and the $y\text{-}$value is the $y\text{-}$intercept. Let's look at the given value. Therefore the $y\text{-}$intercept is $2,$ so the graph intercepts the $y\text{-}$axis at the point $(0,2).$

Graph

We now have enough information to graph the function. To start, plot the $y\text{-}$intercept and one other point using the slope we found above. By connecting these points with a line, we will form the graph of our equation.

$x\text{-}$intercept

Looking at our graph, we can also identify the $x\text{-}$intercept of this function.

The $x\text{-}$intercept of the function lies at the point $(3,0),$ so the $x\text{-}$intercept is $3.$