Chapter 9.5, Problem 31IP

To determine

To graph the equation using slope and y-intercept.

Explanation of Solution

Given information:

The given equation is:

  $\text{x}+\text{4y}=0$

Graph:

The equation is written as:

  $\begin{array}{l}\text{x}+\text{4y}=0\\ \text{4y}=\text{x}+0\left[\text{Subtracting both sides by x}\right]\\ \text{y}=\frac{-\text{x}}{4}\text{+0 }\left[\text{Divide both sides by 4}\right]\\ \text{y}=-\frac{1}{4}\text{x}+0\left[\text{Write the equation in the form y}=\text{mx}+\text{c}\right]\end{array}$

The slope of the equation is $-\frac{1}{4}$ and the y-intercept is $0$ .

Graph the y-intercept at $\left(0,0\right)$ .

Using the slope $-\frac{1}{4}$ locate another point on the line.

Move $\text{y}$ down by $\text{1 unit}$ and move $\text{x}$ right by $4\text{ units}$ .

The other point is $\left(4,-1\right)$ .

Draw a line through the two points.

The graph is: