P 2 Linear Models Rates of Change 1

P. 2 Linear Models & Rates of Change 1. Find the slope of a line passing thru 2 points. 2. Write the equation of a line with a given point and slope. 3. Interpret slope as a ratio or as a rate in a real-life application. 4. Sketch the graph of a linear equation. 5. Write equations of lines that are parallel or perpendicular to a given line.

The Slope of a Line • Definition. The slope m of the nonvertical line passing through (x 1, y 1) and (x 2, y 2) is • Slope is undefined for vertical lines.

Equations of Lines • Point-slope form: y – y 1 = m(x – x 1) • Slope-intercept form: y = mx + b • General form: Ax + By + C = 0 (or, Ax + By = C, where A, B ≠ 0) • Vertical line: x = a • Horizontal line: y = b

Ratios and Rate of Change • The slope of a line can be interpreted as either a ratio or a rate. • If x and y are of the same unit, then the slope has no unit and is a ratio. • If x and y are of different units, then the slope is a rate, or rate of change. • The average rate of change is always calculated over an interval.

Parallel and Perpendicular Lines • Two distinct nonvertical lines are parallel if and only if their slopes are equal, i. e. , m 1 = m 2. • Two distinct nonvertical lines are perpendicular if and only if their slopes are negative reciprocals of each other, i. e. , m 1 m 2 = - 1.