Chapter 1.3, Problem 22E

To determine

To graph: the equation, $2x+5y=8$

Answer to Problem 22E

  

Explanation of Solution

Given information:

  $2x+5y=8$

The equation can be rewritten in slope intercept form as follows:

  $\begin{array}{l}5y=-2x+8\\ y=-\frac{2}{5}x+\frac{8}{5}\left(\mathrm{Rewritten}inslope-intercept\text{ form}\right)\end{array}$

Calculation:

The above equation is already in slope intercept form. Now find value of y , by substituting different value of x.

Put $x=2$ in the slope intercept equation and simplify it as follows:

  $\begin{array}{c}y=-\frac{2}{5}\left(2\right)+\frac{8}{5}\\ y=-\frac{4}{5}+\frac{8}{5}\\ =\frac{4}{5}\end{array}$

So, the first coordinate is $\left(2,\frac{4}{5}\right)$ .

Put $x=-2$ in the slope intercept equation and simplify it as follows:

  $\begin{array}{c}y=-\frac{2}{5}\left(-2\right)+\frac{8}{5}\\ y=\frac{4}{5}+\frac{8}{5}\\ =\frac{12}{5}\end{array}$

So, the second coordinate is $\left(-2,\frac{12}{5}\right)$ .

Now, graph the line straight to these points, and it will be formed as follows: