R
Rishtaara
Mathematics from Zero
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.