Exercise 47 Page 160

We will graph this equation by finding and plotting its intercepts. Then, we will connect them with a line. To find the $x\text{-}$ and $y\text{-}$intercepts, we will need to substitute $0$ for one variable and solve. After that, repeat for the other variable.

Finding the $x\text{-}$intercept

Think of the point where the graph of an equation crosses the $x\text{-}$axis. The $y\text{-}$value of that $(x,y)$ coordinate pair is equal to $0,$ and the $x\text{-}$value is the $x\text{-}$intercept. To find the $x\text{-}$intercept of the given equation, we should substitute $0$ for $y.$ Then, solve for $x.$ An $x\text{-}$intercept of $4.5$ means that the graph passes through the $x\text{-}$axis at the point $(4.5,0).$

Finding the $y\text{-}$intercept

Let's use the same concept to find the $y\text{-}$intercept. Consider the point where the graph of the equation crosses the $y\text{-}$axis. The $x\text{-}$value of the $(x,y)$ coordinate pair at the $y\text{-}$intercept is $0.$ Therefore, substituting $0$ for $x$ will give us the $y\text{-}$intercept. A $y\text{-}$intercept of $\text{-}2.25$ means that the graph passes through the $y\text{-}$axis at the point $(0,\text{-}2.25).$

Graphing the Equation

We can now graph the equation by plotting the intercepts and connecting them with a line.