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$\left(-5,3\right)$.

Short answer

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

Step-by-step solution

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.