Chapter 1.1, Problem 94AYU

In Problems 91-98, graph each equation using a graphing utility. Use a graphing utility to approximate the intercepts rounded to two decimal places. Use the TABLE feature to help to establish the viewing window.

$4x+5y=82$

To determine

To graph: The equation $4x +5y =82$ and approximate the intercepts rounded to two decimal places.

Answer to Problem 94AYU

$x\text{ intercept is }20.5\text{ and }y\text{ intercept is }16.4$

Explanation of Solution

Given:

The equation $4x +5y =82$.

Interpretation:

$4x +5\mathrm{y }-4x =82-4x$

Subtract $4x$ from both sides.

$5y =82-4x$

Divide both sides by 5.

$y = \frac{82 - 4x}{5}$

We are now ready to verify using graphing utility.

$x =-2$	$y = \frac{82 - 4\left(-2\right)}{5} = \frac{82 + 8}{5} = \frac{90}{5} = 18$
$x =-1$	$y = \frac{82 - 4\left(-1\right)}{5} = \frac{82 + 4}{5} = \frac{86}{5} = 17.2$
$x =0$	$y = \frac{82 - 4\left(0\right)}{5} = \frac{82 - 0}{5} = \frac{82}{5} = 16.4$
$x =1$	$y = \frac{82 - 4\left(1\right)}{5} = \frac{\mathrm{82 }-\mathrm{ 4}}{5} = \frac{78}{5} = 15.6$
$x =2$	$y = \frac{82 - 4\left(2\right)}{5} = \frac{82 - 8}{5} = \frac{74}{5} = 14.8$
$y = 0$	$0 = \frac{82 - 4x}{5},$ $\mathrm{82 }-\mathrm{ 4}x = 0,$ $82 = 4x,$ $x = \frac{82}{4} = 20.5$

$x$ intercept is $20.5$ and $y$ intercept is $16.4$