Question

Determine whether the two line are parallel, perpendicular or neither.

x-3y=6

y=1/3x+4

Answer 1

Lines parallel will have the SAME slope.

Lines perpendicular will have OPPOSITE RECIPROCAL slopes.

Let’s first make sure the equations are in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept.

Of the two equations given, only the top isn’t in the form y=mx+b.

x-3y=6, subtract the x

=> -3y=-x+6, divide by -3 both sides

=> y= (1/3)x-2, Now we are in slope-intercept form

As we can see the slopes are equal 1/3=1/3, which makes these lines PARALLEL.