Question

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

$(0,-2)\mathrm{and}(-5,-3)$

Short answer

The equation obtained is:$\mathbf{y}=\frac{1}{5}\mathbf{x}-2$

Step-by-step solution

Step 1. Given Data

Points:$(0,-2)\mathrm{and}(-5,-3)$

Step 2. Finding the slope using given points

The slope of the line through$(0,-2)\mathrm{and}(-5,-3)$:

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

Step 3. Point slope form. 

Choose one point,

let's take point$(0,-2)$

Now,

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

$$\begin{gathered} \mathrm{y}-{\mathrm{y}}_1=\mathrm{m}(\mathrm{x}-{\mathrm{x}}_1) \\ \mathrm{y}-(-2)=\frac{1}{5}(\mathrm{x}-0) \\ \mathrm{y}+2=\frac{1}{5}\mathrm{x} \end{gathered}$$

Step 4. Converting equation in slope-intercept form.

$$\begin{gathered} \mathrm{y}+2=\frac{1}{5}\mathrm{x} \\ \mathbf{y}\mathbf{=}\frac{\mathbf{1}}{\mathbf{5}}\mathbf{x}\mathbf{-}\mathbf{2} \end{gathered}$$