Question

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

Answer 1

`y = (1)/(3)x-4`

Explanation:

Step 1: Solve for y in the first equation

`3y - x = -12`

`3y - x + x = -12 + x`

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

`y = (1)/(3)x - 4`

Step 2: Determine the important aspects

We know that our line is parallel to the other line that has a slope of 1/3 which means that our slope is also going to be 1/3. We also know that our line crosses the point (18, 2) which means that we can use the point slope form to determine our equation

Point Slope Form →
`(y-y_1) = m(x - x_1)`

Step 3: Plug in the information and solve

`(y-2) = (1)/(3)(x - 18)`

`y - 2 = (1)/(3)x - 6`

`y - 2 + 2 = (1)/(3)x - 6 + 2`

`y = (1)/(3)x-4`

Answer:
`y = (1)/(3)x-4`