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Answer 1 · 2016-11-30T08:31:21

$y = \frac{5}{2} x - \frac{19}{2}$ $y=5/2x-19/2$

Or $5 x - 2 y = 19$ $5x -2y = 19$

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

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

Rearranging the equation; $2 y = 5 x - 2; y = \frac{5}{2} x - 1$ $2y=5x-2 ; " "y= 5/2x-1$

Here $m = \frac{5}{2}$ $m= 5/2$ , the slope of the required line
(since new line is PARALLEL the slope is the same)

$y = \frac{5}{2} x + n$ $y=5/2x+n$ where n is a numerical constant.

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

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

$- 2 = \frac{5 (3)}{2} + n \to n = - 2 - \frac{15}{2} = - \frac{19}{2}$ $-2=(5(3))/2 +n " " rarr n=-2-15/2=-19/2$

$\to y = \frac{5}{2} x - \frac{19}{2}$ $rarr y=5/2x-19/2" "$ this is slope-intercept form

Multiplying by 2 to eliminate the denominator;

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