Q 25. - 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.

Perpendicular to the line $3x-y=-4$ containing the point $\left(-2,4\right)$ .

Step-by-Step Solution

Answer

Equation of line is $3x+y=-2$. The graph for the equation is shown below.

Step 1. Given information .

Consider the given equation $3x-y=-4$ and point $\left(-2,4\right)$.

Step 2. Formula used.

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

For two lines to be perpendicular $m_1{m}_2=-1$.

Rewrite the given equation in slope intercept form to find $m_1$.

$$\begin{gathered} 3x-y=-4 \\ y=3x+4 \\ {m}_1=3 ,b=4 \end{gathered}$$

Substitute the value of$\left(x ,y \right)$ to find $m_2$.

$$\begin{gathered} y=m_{2}x+b \\ 4=-2m_2-2 \\ {m}_2=-3 \end{gathered}$$

   

Step 3 . Formula used.

The formula used to find equation of line is $y-y_1=m\left(x-x_1\right)$.

$$\begin{gathered} y-4=-3\left(x+2\right) \\ 3x+y=-2 \end{gathered}$$

Step 4. Plot the graph .

The graph for the equation $3x-y=-4$shown below .