Question

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

y=?

Show Steps Please

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 = (-12 +x)/(2)`

`y = -6 + (x)/(2)`

Your slope is
`(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
`(1)/(2)`

y = mx + b

`y = (1)/(2)x + b`

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

`y = (1)/(2)x + b`

`2 = (1)/(2)(18) + b`

2 = 9 + b Subtract 9 on both sides

2 - 9 = 9 - 9 + b

-7 = b

Your equation is:

`y =(1)/(2)x - 7`