Chapter 2 – Linear Equations and Functions 2.3 – Slope and Rate of Change

In this section we will review: –Finding and using the slope of a line

2.3 – Slope and Rate of Change What is slope? Slope – ratio of the line’s vertical change (rise) to its horizontal change (run) –CANNOT be a vertical line

2.3 – Slope and Rate of Change Just like you need two points to determine a line, you need two points to find the slope of a line. You can use any two points on the line.

2.3 – Slope and Rate of Change The slope m of a nonvertical line passing through the points (x 1, y 1 ) and (x 2, y 2 ) is given by the formula:

2.3 – Slope and Rate of Change Example 1 –Find the slope of the line passing through (-3, 2) and (5, -1).

2.3 – Slope and Rate of Change Example 2 –Find the slope of the line passing through (-3, -3) and (3, 1).

2.3 – Slope and Rate of Change Types of slope –Positive slope–Negative slope

2.3 – Slope and Rate of Change Types of slope –Zero slope–Undefined Slope

2.3 – Slope and Rate of Change Example 3 –Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. (6, 13), (-8, 13) (-3, 5), (3, 10)

2.3 – Slope and Rate of Change Example 4 –Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. (3, -8), (5, 6) (-4, 1), (-2, 11)

2.3 – Slope and Rate of Change Example 5 –Tell which line is steeper: Line 1: through (-5, 4) and (2, 10) or Line 2: through (6, -2) and (-2, -8)

2.3 – Slope and Rate of Change Example 6 –Tell which line is steeper: Line 1: through (1, 9) and (5, 3) or Line 2: through (-1, 3) and (1, -1)

2.3 – Slope and Rate of Change Example 7 –The temperature of heated chocolate is 185°F. Fifteen minutes later, the temperature of the chocolate is 140°F. Find the average rate of change in the temperature of the chocolate.

2.3 – Slope and Rate of Change Example 8 –A town’s building codes require the roof of a house to have a minimum slope, or pitch. To comply, a roof must rise at least 1 foot for every 3 horizontal feet. Does the roof of the house shown in the diagram comply with the code?

2.3 – Slope and Rate of Change HOMEWORK Worksheet 2.3