Chapter 3.1, Problem 55PPS

To determine

To Graph: The equation $y=\frac{1}{4}x-3$ by using x- and y-intercepts.

Explanation of Solution

Given information:

The given equation $y=\frac{1}{4}x-3$

Calculation:

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

  $\begin{array}{l}y=\frac{1}{4}x-3\\ 0=\frac{1}{4}x-3\end{array}$

(Replace y by 0)

  $0+3=\frac{1}{4}x-3+3$

(Adding 3 on both sides)

  $3=\frac{1}{4}x$

(Simplify)

  $3\cdot 4=\frac{1}{4}x\cdot 4$

(Multiply 4 on both sides)

  $x=12$

(Simplify)

The x-intercept is 12. This means that the graph intersects the x-axis at $\left(12,0\right)$ .

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

  $\begin{array}{l}y=\frac{1}{4}x-3\\ y=\frac{1}{4}\left(0\right)-3\end{array}$

(Replace x by 0)

  $y=-3$

(Simplify)

The y-intercept is -3. This means the graph intersects the y-axis at $\left(0,-3\right)$ .

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