Question

What is the slope of a line parallel to `3x+4y=12`?

Answer 1

In this problem we must first find the slope of the given line. Also note that parallel lines have the same slope.

We have 2 options:

1) Manipulate this equation from standard form to slope intercept form, `y=mx+b`, where `m` is the slope.

2) The slope can be found using the following expression, `-A/B`, when the equation is standard form.

OPTION 1:

`3x+4y=12`

`4y=12-3x`

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

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

`y=-3/4x+3 -> slope = -3/4`

OPTION 2:

`Ax+By=C`

`3x+4y=12`

`slope=-A/B=-3/4`

A line parallel to `3x+4y=12` must have a slope of `-3/4`.