Question

What is an equation of the line that passes through the point (− 2, 5) and is parallel to the line 3x + 4y = 12 ?

Answer 1

Answer:
`y=-(3)/(4) x+3.5` or
`y=-(3)/(4)x+(7)/(2)`

Explanation:

A parallel line has the same slope and different y-intercepts.

Let's change our equation to slope-intercept.

`3x+4y=12`

`4y=12-3x`

`y=(12-3x)/(4) =3-(3)/(4)x`

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

Now that we know our slope is -3/4, we know the equation will have -3/4 as the slope. Let's leave b blank so that we can find the y-intercept of the parallel line.

`5=-(3)/(4)(-2)+b`

`5=(3)/(2) +b`

`3.5=b`

Our parallel equation is
`y=-(3)/(4)x+3.5` or
`y=-(3)/(4) x+(7)/(2)`