Exercise 61 Page 10

To determine the $x\text{-}$ and $y\text{-}$intercepts of a line, we 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 $y$-value of that $(x,y)$ coordinate pair is $0,$ and the $x$-value is the $x\text{-}$intercept. To find the $x\text{-}$intercept of the equation, we should substitute $0$ for $y$ and solve for $x.$ An $x\text{-}$intercept of $\frac{1}{3}$ means that the graph passes through the $x\text{-}$axis at the point $(\frac{1}{3},0).$

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