Question

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

Answer 1

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.