Exercise 59 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 $0$ means that the graph passes through the $x\text{-}$axis at the point $(0,0).$

Finding the $y\text{-}$intercept

We could use the same concept to find the $y\text{-}$intercept, but take a close look at the given equation. The given equation is in slope-intercept form, $y=mx+b.$ For an equation in this form, we know that the constant $b$ represents the $y\text{-}$intercept. Therefore, the $y\text{-}$intercept is $0,$ and the graph passes through the $y\text{-}$axis at the point $(0,0).$