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).
