Question

4. Write the equation of a line that passes through the point (-8, 2) and is parallel to the

line 3x – 2y = 12.​

Answer 1

3x - 2y = - 28

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x - 2y = 12 ( subtract 3x from both sides )

- 2y = - 3x + 12 ( divide all terms by - 2 )

y =
`(3)/(2)` x - 6 ← in slope- intercept form

with slope m =
`(3)/(2)`

Parallel lines have equal slopes, thus

y =
`(3)/(2)` x + c ← is the partial equation

To find c substitute (- 8, 2) into the partial equation

2 = - 12 + c ⇒ c = 2 + 12 = 14

y =
`(3)/(2)` x + 14 ← equation in slope- intercept form

Multiply through by 2

2y = 3x + 28 ( subtract 2y from both sides )

0 = 3x - 2y + 28 ( subtract 28 from both sides )

- 28 = 3x - 2y , that is

3x - 2y = - 28 ← equation in standard form