Question

Ine L has equation 2x - 3y = 5. Line M passes through the point (3, -10) and is parallel to line L. Determine the equation for line M.
a.2x + 3y = -24
b.2x - 3y = 36
c.2x - 3y = -10
d.3x + 2y = -24

Answer 1

First of all, let's find the slope of line L. To find the slope of a line, you write it in the explitic form $y = mx+q$, and consider the coefficient $m$. So, we have

$2x - 3y = 5 \iff 3y = 2x-5 \iff y = \dfrac{2}{3} x - \dfrac{5}{3}$

So, the slope of line L is 2/3.

Two lines are parallel if they have the same slope. So, line M has slope 2/3 as well, and we know that it passes through the point (3, -10).

When you are given the slope $m$ and a point $(x_0,y_0)$ of a line, its equation is given by

$y-y_0=m(x-x_0)$

So, if you plug your values, you have

$y+10 = \dfrac{2}{3}(x-3)$

which you can simplify into

$y+10 = \dfrac{2}{3}x-2$

$y = \dfrac{2}{3}x-12$