Intermediate Algebra (12th Edition)

$x\text{-intercept: } \left( 10,0 \right) \\y\text{-intercept: } (0,4)$
$\bf{\text{Solution Outline:}}$ Use the definition of intercepts to find the $x$- and $y$-intercepts of the given equation, $2x+5y=20 .$ Then plot the points corresponding to the intercepts and connect these with a line to get the graph. $\bf{\text{Solution Details:}}$ The $x$-intercept is the value of $x$ when $y=0.$ Substituting $y=0$ in the given equation, then \begin{array}{l}\require{cancel} 2x+5y=20 \\\\ 2x+5(0)=20 \\\\ 2x+0=20 \\\\ 2x=20 \\\\ x=\dfrac{20}{2} \\\\ x=10 .\end{array} Hence, the $x$-intercept is $\left( 10,0 \right) .$ The $y$-intercept is the value of $y$ when $x=0.$ Substituting $x=0$ in the given equation, then \begin{array}{l}\require{cancel} 2x+5y=20 \\\\ 2(0)+5y=20 \\\\ 0+5y=20 \\\\ 5y=20 \\\\ y=\dfrac{20}{5} \\\\ y=4 .\end{array} Hence, the $y$-intercept is $(0,4) .$ Connecting the following intercepts, \begin{array}{l}\require{cancel} x\text{-intercept: } \left( 10,0 \right) \\y\text{-intercept: } (0,4) ,\end{array} gives the graph of the given equation.