Q 19 - Precalculus Enhanced with Graphing Utilities

Question

Find an equation of the line having the given characteristics. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer. Graph the line.

Slope $=0$; containing the point $\left(-5,4\right)$.

Step-by-Step Solution

Answer

The required equation of line is :-

$y=4$.

The graph of the line is :-  

Step 1. Given Information

We have given the following characteristics of a line :- 

Slope $=0$, containing the point $\left(-5,4\right)$.

We have to fine the equation of this line.

Also we have to graph the line.

By applying point slope form, we will find the equation of line. 

Step 2. To find Equation of Line

Slope of the line is $m=0$.

Also we have given a point $\left(-5,4\right)$, that is contained by the line.

By point-slope form, we have if a line has slope $m$, passing through a point $\left(x_1,y_1\right)$, then the equation of line is :-

$y-y_1=m\left(x-x_1\right)$.

So that the equation of given line with slope $m=0$, containing point $\left(-5,4\right)$ is :-

$y-4=0(x+5)$.

We can simplify it as following :-

$$\begin{gathered} y-4=0 \\ \Rightarrow y=4 \end{gathered}$$

This is the required equation of line.

Step 3. Graph the line

The equation of line is :-  

$y=4$.

By using graphing utility, we can graph it as following :-