Chapter 3.1, Problem 28PPS

To determine

To Graph: The equation $y=8-6x$ by using x- and y-intercepts.

Explanation of Solution

Given information:

The given equation $y=8-6x$ .

Calculation:

To find the x-intercept, let $y=0$

  $\begin{array}{l}y=8-6x\\ 0=8-6x\end{array}$

(Replace y by 0)

  $0-8=8-8-6x$

(Subtract 8 on both sides)

  $-8=-6x$

(Simplify)

  $-\frac{6x}{6}=-\frac{8}{6}$

(Divide both sides by 6)

  $\begin{array}{l}-x=-\frac{8}{6}\\ -x=-\frac{4}{3}\end{array}$

(Simplify)

  $-x\left(-1\right)=\left(-1\right)\left(-\frac{4}{3}\right)$

(Multiply -1 on both sides)

  $x=\frac{4}{3}$

(Simplify)

Or

  $x=1.33$

The x-intercept is 1.33. This means that the graph intersects the x-axis at $\left(1.33,0\right)$ .

To find the y-intercept, let $x=0$

  $\begin{array}{l}y=8-6x\\ y=8-6\left(0\right)\end{array}$

(Replace x by 0)

  $y=8$

(Simplify)

The y-intercept is 8. This means the graph intersects the y-axis at $\left(0,8\right)$ .

Plot these two points and then draw a line through them.