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 = (2)/(3) x - (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 = (2)/(3)(x-3)`

which you can simplify into

`y+10 = (2)/(3)x-2`

`y = (2)/(3)x-12`