Question

Plz help, 15 points!

Answer 1

Answer:

$2x+3y=-6$

Step-by-step explanation:

Let the line is $y=mx+b$ where $m$ is slope and $b$ is $y-intercept$.

The line is parallel to $2x+3y=3$, slope of both the lines will be same.

Find the slope of $2x+3y=3$

$3y=3-2x\\y=-\frac{2}{3}x+1$

Slope of line$=-\frac{2}{3}$

$m=-\frac{2}{3}$

So the line will be $y=-\frac{2}{3}x+b$

It passes through $(3,-4)$.

$-4=-\frac{2}{3}\times 3+b\\-4=-2+b\\b=-2$

Hence the line is $y=-\frac{2}{3}x-2$

$y=-\frac{2}{3}x-2\\3y=-2x-6\ \ \ \ \ \ \ (Multiply both sides by 3)\\2x+3y=-6$