Interpreting the slope of a line before graphing

by Frogo
(USA)

Question

How can you tell if two equations are parallel or intersecting before graphing them? For example, do y = x or y = x + 2 intersect?

Answer

STEP 1:   You are given equation of two lines. The most important factor which decides whether two lines are parallel or intersecting is the slope. Remember that parallel lines have the same slope. Also, when two lines are parallel, they do not intersect anywhere.

Since the two equations are already in the slope-intercept form
(y = mx + b), you can easily find their slopes.

Make a note of what each variable in the equation stands for:
STEP 2:    Compare with the standard form.
Both the lines seem to have the same slope, 1. This suggests that they are parallel to each other, and hence do not intersect.