Linear Models & Rates of Change (Precalculus

Review 2)

September 9th, 2015

I. The Slope of a Line

Def: slope = m = y/ x = (y2 - y1)/(x2 - x1)

*slope of vertical lines is undefined

II. Equations of Lines

Point-Slope Equation of a Line:

y - y1 = m(x - x1)

Ex. 1: Find the equation of the line that has a slope of -5 and passes through the point (2, -3).

III. Ratios & Rates of Change

The slope of a line on the x- and y-axes that have equal units of measure is a ratio. When the x- and y-axes have different units of measure, the slope can be interpreted as the rate of change.

IV. Graphing Linear Models

Slope-Intercept Equation of a Line:

y = mx + b

slope y-intercept

*Other Equations of Lines:1. General Form: Ax + By + C = 02. Vertical Line: x = a3. Horizontal Line: y = b

V. Parallel & Perpendicular Lines

Parallel lines have equal slopes (m1 = m2).

Perpendicular lines have opposite reciprocal slopes (m1 = -1/m2).