Graphing Linear Equations

Pre-Algebra · Axiom Academy

A straight line is pinned down by just two points — so every method for graphing y = mx + b is really a way to find two good points. The most direct method, and it works for any linear equation: pick a few x -values, substitute each into the equation to get y , plot the resulting points, and draw the line through them. Watch the cursor below step through x = -1, 0, 1, 2, 3 for y = 2x - 3 — each row's y is computed, then its point lands on the grid. Each x in, each y out — five points on the line Choose a few x -values (3 to 5 is plenty). Substitute each x into the equation to find its y . Plot each (x, y) point on the coordinate plane. Draw a straight line through the points. A line crosses each axis exactly once, and those two crossing points are often the easiest two to find. Setting x = 0 gives the y -intercept ; setting y = 0 gives the x -intercept . The animation finds both for 3x + 2y = 6 , then draws the line straight through them. When the equation already reads y = mx + b , the two numbers hand you the graph directly. The constant b is the y -intercept — your first point. The coefficient m is the slope , the rise over the run — your staircase to the second point. For : start at (0,-1) , run right 2 , rise up 3 . b = where you start · = how you step

This is the written version of the interactive lesson above. See the full Pre-Algebra course.