Question

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

Answer 1

`y=-2.5x-9`

Explanation:

One is given the following equation.

`5x + 2y = 12`

The problem asks one to find a line that is parallel to this one, and passes through the point:
`(-2, 4)`. The equation of the given line is in the standard format. The easiest approach to solve this problem is to change the equation of the given line into the slope-intercept format. The solve intercept format follows the following general equation:

`y=mx+b`

Where (m) is the slope of the line and (b) is the y-intercept. Manipulate the given equation such that it follows this format:

`5x+2y=12\\2y=12-5x\\y=6-2.5x\\\\y=-2.5x+6`

One property of parallel lines is that they have the same slope. Therefore, if one uses the slope-intercept format to represent the slope of the parallel line, then one can state the following:

`y=-2.5x+b`

Substitute a given point on this line (
`-2,4`) , and solve for (b) to find (b):

`y=-2.5x+b\\(4)=-2.5(-2)+b`

Simplify,

`4=-2.5(-2)+b\\-4=5+b`

Inverse operations,

`-4=5+b\\-9=b`

Substitute this back into the equation in slope-intercept form to find the equation of the parallel line:

`y=-2.5x-9`