# What best describes the relationship between the lines with equations y+ 3x= 10 and 2y= -6x + 4?

Oct 23, 2016

The relationship between $y + 3 x = 10$ and $2 y = - 6 x + 4$ is that they are parallel lines.

#### Explanation:

The easiest way to see the relationship between the two lines is to transform them both into slope-intercept form, which is $y = m x + b$.

Equation 1:
$y + 3 x = 10$
$y + 3 x - 3 x = - 3 x + 10$
$y = - 3 x + 10$

Equation 2:
$2 y = - 6 x + 4$
$\frac{2 y}{2} = \frac{- 6 x + 4}{2}$
$y = - 3 x + 2$

In this form, we can easily identify that both lines have a slope of $- 3$, but that they have different $y$-intercepts. Lines will equal slopes but different $y$-intercepts are parallel.

Therefore, the lines are parallel.