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

1 Answer
Oct 23, 2016

The relationship between #y + 3x = 10# and #2y = -6x + 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 = mx + b#.

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

Equation 2:
#2y = -6x + 4#
#(2y)/2 = (-6x + 4)/2#
#y = -3x + 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.