L3 · Slope: Rise over Run, and Slope as Rate of Change
“I can calculate the slope of a line or segment from any two points, explain the slopes of horizontal and vertical lines, find another point on a line from its slope, and interpret slope as a rate of change with units.”
Find the slope of the line through (2, 3) and (6, 11). Step 1: Rise = change in y = 11 - 3 = 8. Run = change in x = 6 - 2 = 4. Step 2: Slope m = rise / run = 8 / 4 = 2. Step 3: Sanity check the sign - as x increases, y increases, so a positive slope is right. Each step of 1 in x adds 2 to y. Two special cases: through (1, 4) and (6, 4) the rise is 0, so the slope is 0 (a horizontal line). Through (3, 7) and (3, -2) the run is 0, and division by zero is impossible - the slope is undefined (a vertical line). Say it plainly: slope = (change in y) / (change in x), computed in the same order for both.
The slope through (0, 5) and (5, 0) must be negative because...
Find the slope through (1, 6) and (4, 15). -> m = (15 - 6) / (4 - 1) = 9 / 3 = 3
"The slope through (2, 1) and (6, 9): rise = ___, run = ___, slope = ___." -> rise 8, run 4, slope 2
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.