Chapter 1, Problem 24RE

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

To determine

To find: The equation of a line containing the point $\left(-5,3\right)$ and parallel to the line $2x-3y=-4$. To also sketch a graph of the equation.

Answer to Problem 24RE

Solution:

The general form of equation of the line is $2x-3y=-4$.

Explanation of Solution

Given:

The points $\left(-5,3\right)$ and the line $2x-3y=-4$

Formula used:

Point slope form of an equation of a line.

$(y-y₁)=m(x-x₁)$

Calculation:

To find the slope, write the given line $2x-3y=-4$, in the form of $y=mx+c$.

$2x-3y-2x=-4-2x$  &nbspSubtract $2x$ from both sides.

$-3y=-2x-4$

$y=\frac{-2}{-3}x+\frac{-4}{-3}$  &nbspDivide both sides by $–3$.

$y=\frac{2}{3}x+\frac{4}{3}$

Hence the slope $m=\frac{2}{3}$

Now using this slope $m=\frac{2}{3}$ and the point $\text{A}\left(-5,3\right)$, the equation can be found.

$y-3=\frac{2}{3}\left(x-\left(-5\right)\right)$

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

$3\left(y-3\right)=2\left(x+5\right)$

$3y-9=2x+10$

$3y-9-2x=2x+10-2x$

$-2x+3y-9=10$

$2x-3y+9=-10$  &nbspMultiply $\text{−1}$ to both sides.

$2x-3y+9-9=-10-9$  &nbspSubtract 9 from both sides.

$2x-3y=-19$

The general form of equation of the line is $2x-3y=-19$.