# The Graph of an Equation - Houston Community College 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 reallife 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 (x1, y1) and (x2, y2) is Slope is undefined for vertical lines. Equations of Lines Point-slope form: y y1 = m(x x1)

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., m1 = m2. Two distinct nonvertical lines are perpendicular if and only if their slopes are negative reciprocals of each other, i.e., m1 m2 = - 1.