Question

In the following exercises, find the equation of a line containing the given points. Write the equation in slope-intercept form.

$(3,-4)\mathrm{and}(5,-4)$

Short answer

The equation obtained is:$\mathrm{y}=-4$

Step-by-step solution

Step 1. Given Data

Points:$(3,-4)\mathrm{and}(5,-4)$

Step 2. Finding the slope using given points

The slope of the line through $(3,-4)\mathrm{and}(5,-4):$

$$\begin{gathered} \mathrm{m}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}\left(1\right) \\ \mathrm{where}, \\ {\mathrm{y}}_2=-4 \\ {\mathrm{y}}_1=-4 \\ {\mathrm{x}}_2=5 \\ {\mathrm{x}}_1=3 \\ \mathrm{Putting}\mathrm{values}\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ \mathrm{m}=\frac{-4-(-4)}{5-3}=\frac{-4+4}{2}=0 \\ \mathrm{m}=0 \end{gathered}$$

Step 3. Point slope form. 

Choose one point

let's take point$(3,-4)$

Now,

Substitute the values in the point-slope form which is:

$$\begin{gathered} \mathrm{y}-{\mathrm{y}}_1=\mathrm{m}(\mathrm{x}-{\mathrm{x}}_1) \\ \mathrm{y}-(-4)=0(\mathrm{x}-3) \\ \mathrm{y}+4=0 \end{gathered}$$

Step 4. Converting equation in slope-intercept form.

$$\begin{gathered} \mathrm{y}+4=0 \\ \mathbf{y}\mathbf{=}\mathbf{-}\mathbf{4} \\ \mathrm{or} \\ \mathrm{y}=0\mathrm{x}-4 \end{gathered}$$