Lesson 9 of 16Article19 min
Linear Graphs & Slope
Every point (x, y) pairs an input with an output. A linear relationship graphs as a straight line — constant rate of change.
The coordinate plane
Every point (x, y) pairs an input with an output. A linear relationship graphs as a straight line — constant rate of change.
Reading m and b
- m is rise/run: how much y changes when x increases by 1.
- b is the y-intercept: where the line crosses the y-axis (x = 0).
- Horizontal line: m = 0 (y = constant). Vertical line: undefined slope (x = constant).
- Parallel lines share m; perpendicular lines have slopes whose product is −1 (neither vertical).
Positive slope rises left→right; negative slope falls left→right. Steeper |m| means faster change.
Worked example
Line through (1, 2) and (4, 8): m = (8−2)/(4−1) = 6/3 = 2. Using point-slope with (1,2): y − 2 = 2(x − 1) → y = 2x.