Graphing Lines
Grades 8–10 Algebra Graphs
Every linear equation draws a straight line. In
y = mx + b: m is the slope
(how steep) and b is the y-intercept
(where it crosses the y-axis).
Slope = rise over run
Slope 2 means "up 2 for every 1 right." Slope −1/2 means "down 1 for every 2 right." Steeper → bigger |m|; downhill left-to-right → negative.
Reading y = mx + b
y = 2x + 1→ crosses y-axis at (0, 1), climbs up 2 per stepy = −x + 4→ crosses at (0, 4), slides downhilly = 3→ flat horizontal line through y = 3
Plot in 3 steps
1) dot the y-intercept b on the y-axis · 2) use slope as a "staircase"
(rise, then run) for a second point · 3) draw through both.
Parallel & perpendicular
Same slope → parallel lines (never meet). Slopes that are negative
reciprocals (2 and −1/2) → perpendicular.
Practice
In y = 3x − 2, the slope is ___
In y = −x + 5, the y-intercept is at y = ___
Lines y = 2x + 1 and y = 2x − 7 are:
A line through (0, 0) and (3, 6) has slope ___
Next: systems of equations · Back: factoring