Graphing inequalities on the coordinate plane means drawing the boundary line for y = mx + b, using a dashed line for strict inequalities and a solid line for ≤ or ≥, then shading the region where the inequality is true. The ACT may ask you to graph a solution, pick the correct graph from four choices, or read an inequality from a shaded region.
Start with the boundary line
Rewrite the inequality as an equation: y = 2x + 1. Plot that line using slope and y-intercept, or two easy points. For y > 2x + 1 or y < 2x + 1, draw a dashed line—the boundary is not included. For y ≥ 2x + 1 or y ≤ 2x + 1, draw a solid line. That matches the open and closed circles on a number line from inequalities on the ACT.
Which side to shade
Pick a test point not on the line—(0, 0) is the usual choice unless the line runs through the origin. Plug it into the original inequality. If it works, shade that side. If not, shade the other side.
Example: y > x + 2. Test (0, 0): is 0 > 0 + 2? No. Shade the side that does not contain the origin—above the line for this slope. Shortcut for y > mx + b: shade above. For y < mx + b: shade below. For x > k: shade right. For x < k: shade left.
Reading graphs on the test
When the question shows four shaded regions, check three things: dashed vs solid, slope direction, and y-intercept. One wrong detail eliminates three choices fast. If the boundary is vertical, x = 3, shade right for x > 3 and left for x < 3.
Systems of inequalities
Graph each inequality and look for the overlap—the region shaded by both. That overlap is the solution set. The ACT usually keeps these to two inequalities, so two boundary lines and one shared region.
Coordinate skills you need
Slope, intercepts, and plotting lines come from coordinate geometry on the ACT. If you can graph y = mx + b confidently, adding the shade step is quick. Review linear inequality solving first in inequalities on the ACT, then practice picking graphs from equations and equations from graphs until the dashed-or-solid check is automatic.
Start practicing
Start with a free diagnostic, then drill your weak spots with 15-question quizzes and track how you're doing across Reading, English, and Math. Compare plans whenever you're ready to go further.
This article offers general ACT prep guidance. The ACT can change from year to year, including its format, scoring, policies, test dates, and fees, so always confirm the latest details on the official ACT website at act.org before you make decisions. ACT® is a registered trademark of ACT, Inc. thirty-six is not affiliated with, endorsed by, or sponsored by ACT.