From Equation to Graph

Algebra 1 · Axiom Academy

A linear equation is a story about a straight line. Here are three reliable ways to turn that story into a picture. The most fundamental method. Pick a few values for x , plug each into the equation to get y , and stamp the resulting (x, y) pair on the grid. Two points already fix the line — a third is just insurance. Choose x, compute y, plot the pair When the equation reads y = mx + b , it hands you two facts for free: where the line starts on the y-axis (the intercept b ) and how steep it climbs (the slope m ). Plot b , then let the slope step you to the next point. Start at b, then rise over run Plot the first point at (0, b) — here (0, 1) . Read m = 2 = 1 as rise 2 , run 1 . The y-intercept is where the line crosses the y-axis — set x = 0 . The x-intercept is where it crosses the x-axis — set y = 0 . Those two axis-crossings are all you need to draw the line, which makes this the natural choice for standard form Ax + By = C . Here is the payoff. Take a single equation and watch all three methods build toward it. The points you stamp, the rise-over-run step, and the two intercepts are different routes — but they all land on the exact same line . Choosing a method is about convenience, never correctness. Three constructions, one graph You now have three reliable ways to turn a linear equation into a graph — and you have seen that they all agree on the same line. Scroll up to revisit any method.

This is the written version of the interactive lesson above. See the full Algebra 1 course.