# How do you graph the line that passes through (0,3) parallel to the graph 6y-10x=30?

Apr 28, 2018

See a solution process below..

#### Explanation:

Recall equation of a line;

$y = m x + c$

Where;

$m = \text{gradient}$

$c = \text{intercept}$

Now given;

$6 y - 10 x = 30$

$6 y = 10 x + 30$

$y = \frac{10}{6} x + \frac{30}{6}$

$y = \frac{5}{3} x + 5$

Gradient $= \frac{5}{3}$

Note: when two lines are parallel to each other, their gradients equals to each other and when the lines are perpendicular to eachother, the multiplication of their gradients equals -1​

Therefore;

Gradient of the second equation $= \frac{5}{3}$

$\left(0 , 3\right)$ let $\left(x , y\right)$ be another points

$\frac{y - 3}{x - 0} = \frac{5}{3}$

Cross multiplying..

$3 y - 9 = 5 x - 0$

$3 y = 5 x + 9$

$3 y - 5 x - 9 = 0$