Question

Question #bc419

Answer 1

`y=5/2x-19/2`

Or `5x -2y = 19`

Explanation:

Conditions:
• Parallel to `5x-2y=2`
• Passes through the point `(3;-2)`

General equation for a line: `y=mx+n` where `m` is the slope of the line.

Rearranging the equation; `2y=5x-2 ; " "y= 5/2x-1`

Here `m= 5/2`, the slope of the required line
(since new line is PARALLEL the slope is the same)

`y=5/2x+n` where n is a numerical constant.

To find `n`, we know the line passes through the given point.

Replacing the values of this point in the equation of the new line:

`-2=(5(3))/2 +n " " rarr n=-2-15/2=-19/2`

`rarr y=5/2x-19/2" "` this is slope-intercept form

Multiplying by 2 to eliminate the denominator;

`2y=5x-19 " or " 5x -2y = 19" "` this is standard form.