Question

What is the equation of the line that is parallel to the line 5X+

2Y= 12 and passage to the point -2, 4

Answer 1

Explanation:

To determine the equation of the line parallel to
`5x + 2y = 12`, we need to first determine the slope of the given line.

A line in slope-intercept form is represented by the following:

`y = mx + b`

where
`m` is the slope of the line and
`b` is the y-intercept.

Rearranging the given line will give us the slope of the line:

`5x + 2y = 12`

`2y = -5x + 12`

`y = -(5)/(2)x + 6`

From this, since we know the lines are parallel, if the slope of the given line is
`-(5)/(2)`, then the slope of the line we are constructing must also be
`-(5)/(2)`.

We can now start to construct the line with the same slope-intercept form:

`y = mx + b`

`y = -(5)/(2)x + b`

To determine the y-intercept,
`b`, we can plug in the point
`(-2, 4)` since we are told from the problem statement that this parallel line runs through it:

`y = -(5)/(2)x + b`

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

`4 = 5 + b`

`b = -1`

Finally, we have our parallel line:

`y = -(5)/(2)x - 1`

If this line needs to be in standard form, we can rearrange it a little:

`2y = -5x - 2`

`5x + 2y = -2`