Exercise 8 Page 159

We will graph this equation by finding and plotting its intercepts, then connecting them with a line. To find the $x\text{-}$ and $y\text{-}$intercepts, we will need to substitute $0$ for one variable, solve, then 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 $y$ and solve for $x.$ An $x\text{-}$intercept of $\frac{1}{2}$ means that the graph passes through the $x\text{-}$axis at the point $(\frac{1}{2},0).$

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 $\text{-}\frac{1}{5}$ means that the graph passes through the $y\text{-}$axis at the point $(0,\text{-}\frac{1}{5}).$

Graphing the Equation

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