Q 24. - 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.

Parallel to the line $2x-3y=-4$containing the point $\left(-5,3\right)$.

Step-by-Step Solution

Answer

Equation of the line is $2x-3y=-19$

Step 1. Given information.

Consider the given equation $2x-3y=-4$ and point $\left(-5,3\right)$.

Step 2. To write the given equation in slope intercept form .

Slope intercept form is $y=mx+c$.

$$\begin{gathered} 2x-3y=-4 \\ -3y=-2x-4 \\ y=\frac{2}{3}x+\frac{4}{3} \end{gathered}$$

The given line has slope $\frac{2}{3}$ and any line that is parallel to this line  will have same slope therefore it is require the point $\left(-5,3\right)$ to be lie on same plane .

Step 3. Find the equation of the line.

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

Substitute the value of $x_{1 } , y_{1 }$and $m$.

$$\begin{gathered} y-3=\frac{2}{3}\left(x+5\right) \\ 2x-3y=-19 \end{gathered}$$

Step 4. Plot the graph.

The graph for the equation $2x-3y=-19$ shown below.