Question

Which equations represents a line that is parallel to 3x-4y=7 and passes through the point (-4,-2)

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange 3x - 4y = 7 into this form

Subtract 3x from both sides

- 4y = - 3x + 7 ( divide all terms by - 4 )

y =
`(3)/(4)` x -
`(7)/(4)` ← in slope- intercept form

with slope =
`(3)/(4)`

• Parallel lines have equal slopes, hence

y =
`(3)/(4)` x + c ← is the partial equation of the parallel line

To find c substitute (- 4, - 2) into the partial equation

- 2 = - 3 + c ⇒ c = - 2 + 3 = 1

y =
`(3)/(4)` x + 1 ← in slope- intercept form

Multiply all terms by 4

4y = 3x + 4 ( subtract 4 from both sides )

4y - 4 = 3x ( subtract 4y from both sides )

- 4 = 3x - 4y, that is

3x - 4y = - 4 ← in standard form