chapter 2 – linear equations and functions 2.3 – slope and rate of change
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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 lineTRANSCRIPT
Chapter 2 – Linear Equations and Functions
2.3 – Slope and Rate of Change
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 (x1, y1) and (x2, y2) 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
HOMEWORKWorksheet 2.3