determine wheter the graphs of the equations are parallel?

Question

y - 2 = -2x
3y - 2 = -6x

how do i solve this ?

Answer 1

y - 2 = -2x
3y - 2 = -6x
then
y = -2x +2 so its slope is = -2
3y = -6x +2
y = -2x + 2/3, so its slope is = -2
therefore the 2 lines are parallel

Answer 2

Hi,
If lines have the same slope, they are parallel. So, one way to determine if they have the same slope if to put the equations in slope-intercept form. That's
y = mx +b (Where m is the slope and b is they y-intercept.)
So, let's put the equations in slope-intercept form.
First one:
y-2 = -2x
y = -2x +2 (Add 2 to both sides of the equation.)

Second one:
3y-2 = -6x
3y = -6x +2 (Add 2 to both sides.)
y = -2x + 1/3 (Divide each term by 3.)
So, m is the same for both equations and, therefore, they are parallel. We don't care what the intercept is.


Hope this helps.
FE

Answer 3

if they are parallel, then the slope is the same

so, first put equations in generic format y = mx+b

1) y = -2x+2

2. 3y = -6x + 2 Divide by 3 y=-2x + 2/3

slopes are both -2; so lines are parallel