# How do you find the equation of the line parallel to 3x + 5y = 11 and has a y-intercept of -6?

Oct 9, 2017

#### Explanation:

The slope of the the straight line equation $3 x + 5 y = 11$ is $\left(- \frac{3}{5}\right)$
Hence the slope of the line parallel is same to the given line i.e,$\left(- \frac{3}{5}\right)$
We can write the equation in the following form slope intercept form i.e, $y = m x + c$
Here $c = - 6$ and $m = - \frac{3}{5}$

The answer is $y = - \frac{3}{5} x - 6 \implies 5 y = - 3 x - 30 \implies 3 x + 5 y = - 30$

Hope it helps...
Thanks you...

Oct 9, 2017

The equation of the line is $y = 3 x + 5 y = - 30$

#### Explanation:

Parallel lines have equal slope. The slope of the line

$3 x + 5 y = 11 \mathmr{and} y = - \frac{3}{5} x + \frac{11}{5} \left[y = m x + c\right]$ is $m = - \frac{3}{5}$

The required line has $y$ intercept of $- 6 \mathmr{and} \left(0 , - 6\right)$

Let the required equation of the line is $y = m x + c$ or

$y = - \frac{3}{5} x - 6$ since $m = - \frac{3}{5} \mathmr{and} c = - 6 \therefore$ The equation

of the line is $y = - \frac{3}{5} x - 6 \mathmr{and} 3 x + 5 y = - 30$

graph{-3/5x-6 [-22.5, 22.5, -11.25, 11.25]} [Ans]