Q22. - 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.

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

Step-by-Step Solution

Answer

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

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.