Question

Write an equation of the line that passes through (18, 2) and is parallel to the line 3y−x=−12

Answer 1

First isolate the "y" in the equation.

2y - x = -12 Add x on both sides

2y - x + x = -12 + x

2y = -12 + x   Divide 2 on both sides to get "y" by itself

$y = \frac{-12 +x}{2}$

$y = -6 + \frac{x}{2}$

Your slope is $\frac{1}{2}$.

For the equation of the line to be parallel to the given equation, the slopes have to be the same. So the parallel line's slope is also $\frac{1}{2}$

y = mx + b

$y = \frac{1}{2}x + b$

To find "b", you plug in the point (18,2) into the equation

$y = \frac{1}{2}x + b$

$2 = \frac{1}{2}(18) + b$

2 = 9 + b Subtract 9 on both sides

2 - 9 = 9 - 9 + b

-7 = b

Your equation is:

$y =\frac{1}{2}x - 7$