Building Linear Equations

Algebra 1 · Axiom Academy

A straight line has a recipe: two numbers, m and b . Watch them build a line, then drive each one yourself. A line is built from just two numbers Every non-vertical straight line — no matter how steep, how flat, or where it sits — is captured by one short equation, y = m x + b . Just two numbers, and the whole infinite line is pinned down. You don't have to take that on faith — first watch the recipe assemble one line, then change each number yourself and see exactly what it does. Watch a line get built in two moves. First the b value drops a starting dot on the vertical axis — that's where the line will cross. Then the m value tilts a line out of that dot to set its steepness. The two numbers together draw y = ½ x + 2 . Set the crossing point, set the steepness — that's the whole line. The steepness is locked (slope m = 1 ). Slide b — or grab the line and drag it up and down. The whole line slides straight up or down, and the spot where it crosses the vertical axis follows b exactly. Try to make it cross at +3 . b is the height where the line meets the y-axis — change it and the line just slides. Now the crossing point is locked ( b = 1 , so the line always passes through (0, 1) ). Slide m and watch the line pivot on that pinned point. Big positive m tilts it steeply uphill; near zero is almost flat; negative tips it downhill. The little wedge shows the rise ÷ run that m measures. m is rise over run — how far the line climbs for every step right.

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