Slope-Intercept Form y = mx + b

Pre-Algebra · Axiom Academy

Why y = mx + b is the easiest way to read a line: m sets the steepness, b sets where it starts. Every linear equation can be written as y = mx + b . The power of this form is that both numbers are something you can see on the graph — there is nothing to compute. m — the slope (how steep the line is) b — the y-intercept (where it crosses the y-axis) In y = 2x + 3 , the slope is m = 2 and the y-intercept is b = 3 . So the line crosses the y-axis at the point (0, 3) , and for every 1 step right it climbs 2 — exactly what the animation traces. 2. The Slope m — Steepness and Direction The slope measures how fast the line rises. Hold the y-intercept fixed and let m change: a bigger m tilts the line up more steeply, and a negative m tips it downhill. The slope is the rise over the run — how far up for each step right. The line rises from left to right. Larger m means a steeper climb — m = 3 is steeper than m = 1 . The line falls from left to right. For each step right, it drops by |m| . — count how far the line goes up for every 1 unit it goes right. Changing only m swings the line around its y-intercept; the crossing point stays put. 3. The Intercept b — and Graphing the Line

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