Divide. Warm-Up Exercises ANSWER 0 undefined ANSWER –1 1. – 7 – – 3 – – 5 – An Internet company had a profit of $2.6 million in retail sales over the last five years. What was its average annual profit? $520,000 ANSWER

Example 1 Find the Slope of a Line Find the slope of the line passing through and. () 5 1,1, – () 2 3,3, 5 – 2 – 3 () 1 – = Substitute values., or 4 3 – 4 3 – = Simplify. SOLUTION = Let and. () x1, y1x1, y1 () x2, y2x2, y2 () 5 1,1, – () 2 3,3, = Rise: Difference of y -values m = – y 2 y 1 – x 2 x 1 Run: Difference of x -values

Example 1 Find the Slope of a Line You can check that the result is the same if you let and. = () x1, y1x1, y1 () x2, y2x2, y2 () 5 1,1, – () 2 3,3, =

Classify Lines Using Slope Example 2 Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. () 1 4,4, – () 1,1, – 2 – () 2 3,3, () 5 3,3, a.b. SOLUTION a. 3 3 – = 1.1. – – 1 – 2 – 1 – () 4 – m == Because m < 0, the line falls. which is undefined. Because m is undefined, the line is vertical. b. m = 3 – 3 2 – 5 = 0 3,,,

Checkpoint Find the slope of the line passing through the given points. Then tell whether the line rises, falls, is horizontal, or is vertical. 1. ANSWER 1 ; rises () 2,2, – 3 – ( ),), 2 3,3, 2. ( ),), 8 1,1, – () 1,1, – 1 – ANSWER undefined slope; is vertical Find and Use Slope

Checkpoint 3. ( ),), 4 5,5, – () 4 1,1, – ANSWER 0 ; is horizontal Find and Use Slope Find the slope of the line passing through the given points. Then tell whether the line rises, falls, is horizontal, or is vertical.

Example 3 Compare Steepness of Lines Tell which line is steeper. Line 1: through and () 2, 5 () 4, 1 – Line 2: through and () 4, 2 () 1, 6 – SOLUTION Line 1 and Line 2 pass through the given points. Slope of line 2: m 2 = – 62 – 4 = () 1 – 5 4 – Slope of line 1: m 1 = – 5 – 1 – 24 = 2 – 6 = – 3

Example 3 Compare Steepness of Lines Both lines have negative slope. Because, line 1 is steeper than line 2. m1m1 m2m2 >

Checkpoint ANSWER line 1 Tell which line is steeper. Line 2: through and 4.Line 1: through and () 1, 5 () 3, 0 – () 2, 6 –– () 4, 1 – ANSWER line 2 5. Line 2: through and Line 1: through and () 5, 5 – () 21, 2 () 2, 27 () 2, 3 Compare Steepness of Lines

Example 4 Slope as a Rate of Change Volcanoes A volcanologist measures the temperature of a lava sample to be 2100°F. Thirty minutes later, the lava sample has cooled to a temperature of 1800°F. Find the average rate of change in the temperature of the sample. SOLUTION Let and. () x1, y1x1, y1 () 0, 2100 = () x2, y2x2, y2 () 30, 1800 = Average rate of change = Change in temperature Change in time – 1800°F – 30 min = 2100°F 0 min – 30 min = 300°F – = 10°F/min

Example 4 Slope as a Rate of Change ANSWER The average rate of change is per minute. On average, the lava cools 10 degrees Fahrenheit each minute. – 10°F

Checkpoint 6. ANSWER 6a. 9.6 million subscribers per yr 6b million subscribers per yr Cellular Phones The estimated number of cellular phone subscribers in the United States was 13 million in 1993, 61 million in 1998, and 219 million in Find the average yearly rate of change in the number of subscribers (a) from 1993 to 1998 and (b) from 1998 to Slope as a Rate of Change