Problem: Determine which two equations represent parallel lines.
Identify slopes
The slope-intercept form is y = mx + b, where m is the slope.
(a) y = -9x + 1 slope m = -9
(b) y = 9x + 1 slope m = 9
(c) y = 1/9 x + 1 slope m = 1/9
(d) y = -9x + 3 slope m = -9
Compare slopes
Parallel lines have equal slopes.
Slopes of (a) and (d) are both -9 = parallel
Other slopes are different = not parallel
Answer:
The parallel lines are (a) y = -9x + 1 and (d) y = -9x + 3