I have tried many times but have failed in all of them. Help!
The question is:
Find the equation of the line passing through the point $(-2,6)$ and parallel to the line with equation $2y-3x=8$. Express the answer in the form of $y=mx+c$.
I have tried making $x$ zero to get the $y$-coordinate and have made $y$ zero to get the $x$-coordinate. I have also tried to change the equation around to $y=mx+c$ form to no success.
Best Answer
You could try this:
Two parallel lines will have the same gradient hence the gradient of the equation of the line passing through $(-2, 6)$ will be $\frac{3}{2}$(see below).
$$ 2y = 3x + 8$$
$$y = \frac{3}{2}x+4$$
Equation of new line(Using $m = \frac{y-y_1}{x-x_1}$):
$$ \frac{3}{2} = \frac{y-6}{x+2}$$
$$3(x+2) = 2(y-6)$$
$$ 2y =3x + 18$$