P.2 Linear Models and Rates of Change Slope: The measure of the number of units a line rises or falls vertically for each unit of horizontal change from right to left (STEEPNESS) Slope is used to denote the _________________ of _________________ of a linear function Slope of a Line The slope of a nonvertical line passing through points (x1 , y1 ) and (x2 , y2 ) is y −y
m = 2 1 = _________________ x2 − x1
Equations of Lines 1. General Form 2. Vertical Line 3. Horizontal Line 4. Point Slope Form 5. Slope Intercept Form EX. Find the equation of a line that has a slope of 3 and passes through the point (1, -­‐2) Ex. The population of Arizona was 1,775,000 in 1970 and 2,718,00 in 1980. Over this time what was the average rate of change of the population? Graphing Linear Models Sketch the graph of each equation a. y= 2x+1 b. y=2 c. 3y + x -­‐ 6=0 Parallel and Perpendicular Lines
1. Two lines are parallel if and only if their slopes are ______________
2. Two lines are perpendicular if and only if their slopes are
____________________
Find the general form of a line passing through the point (2, -1) that is
a. parallel to 2x – 3y = 5
b. perpendicular to 2x – 3y = 5