# Question bc419

Nov 30, 2016

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

Or $5 x - 2 y = 19$

#### Explanation:

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

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

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

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

$y = \frac{5}{2} x + n$ 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:

$- 2 = \frac{5 \left(3\right)}{2} + n \text{ } \rightarrow n = - 2 - \frac{15}{2} = - \frac{19}{2}$

$\rightarrow y = \frac{5}{2} x - \frac{19}{2} \text{ }$ this is slope-intercept form

Multiplying by 2 to eliminate the denominator;

$2 y = 5 x - 19 \text{ or " 5x -2y = 19" }$ this is standard form.