How can you tell if lines are parallel, perpendicular, or neither

Question

by looking at these two equations y=2x+8 and 4x-2y=12 ?

Answer 1

Slope - intercept form line equation is y = mx + b, where m is slope and b is y - intercept.

The two equations are y = 2x + 8 and 4x - 2y = 12.

Write the equations in slope - intercept  form.

y = 2x + 8 and y = 2x - 6.

Compare the above equations in slope - intercept form of a line equation.

Slopes are m₁ = 2 and m₂ = 2.

So, the two lines have same slopes and different y - intercepts.

Since the two lines have same slopes and different y - intercepts, they are parallel lines.