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.

y intercept is $-2$ containing the point$\left(5,-3\right)$.

Short answer

The equation of line is $x+5y=10$and graph for the line as shown below.

Step-by-step solution

Step 1. Given information.

Consider the given$y$intercept and point$\left(5,-3\right)$.

Step 2. Formula used .

The line slope intercept form $y=mx+b$is used to find equation.

Substitute the values of $x,y$and $b$.

$$\begin{gathered} y=mx+b \\ -3=5m-2 \\ m=\frac{-1}{5} \end{gathered}$$

Further simplify to find the equation using line intercept form$y-y_1=m\left(x-x_1\right)$

$$\begin{gathered} y+3=\frac{-1}{5}\left(x-5\right) \\ x+5y=10 \end{gathered}$$

Step 3. Plot the graph 

The graph for the given equation as shown below.