Ch. 5 Vocabulary ) Rate of change 2.) slope

Algebra I 5.1A Rate of Change

Rate of Change

Ex. 1 Cost of pencils Is the rate of change in cost constant with respect to the number of pencils bought? # of pencilsCost ( $)

Ex. 2 Find the rate of change The cost of tickets is $36 for 3 people & $84 for seven people.

Slope The ratio of vertical change (rise) to horizontal change (run).

Ex. 1 Find the slope of the line.

Ex. 2 What is the slope of each line.

Algebra 1 5-1B Slope

Finding the slope of a line Ex. 3 - Find the slope of the line passing through (-2, -4) and (3, -1).

Classification of lines by slope Positive slope – rises from left to rt; m>0 Negative slope – falls from left to rt; m < 0

Classification of lines by slope Zero slope – horizontal line; m = 0 Undefined slope – vertical line; m is undefined

Classifying Lines using slope Ex. 4 Without graphing, tell whether the line through the given points is positive, negative, zero or undefined. a.) (-2, 3), (1, 5) b.) (1, -2), (3, -2)

Assignment

Comparing Steepness For two lines with positive slopes, the line with the greater slope is steeper. For two lines with negative slopes, the line with the slope of greater absolute value is steeper. Reminder: horizontal lines are “flat” and vertical lines are “infinitely steep”

Comparing Steepness of Lines Ex. 3 Tell which line is steeper. Line 1: through (1, -4) and (5, 2) Line 2: through (-2, -5) and (1, -2)

Parallel Lines – same slope

Perpendicular lines – Opposite and reciprocals slope

Classifying Parallel & Perpendicular Lines Ex. 4 Tell whether the lines are parallel, perpendicular, or neither. Line 1: through (1, -2) and (3, -2) Line 2: through ( -5, 4) and (0, 4)

Geometrical use of slope Ex. 5 An escalator in an airport rises 28 ft over a horizontal distance of 48 feet. What is the slope of the escalator?

Slope as a rate of change Ex. 6 Over a 30 day period, the amount of propane in a tank that stores propane for heating a home decreases from 400 gallons to 214 gallons. What is the average rate of change in the amount of propane?

Assignment