divide. warm-up exercises answer 0 undefined answer –1 1. – 7 – 43 8 2. – 3 – 88 5 3. –...
DESCRIPTION
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, =TRANSCRIPT
Divide.
Warm-Up Exercises
ANSWER 0
ANSWER undefined
ANSWER –11. –7–4 3
8
2. –3–8 8
5
3. –5–2 7
5
4. An Internet company had a profit of $2.6 million in retail sales over the last five years. What was its average annual profit?
$520,000ANSWER
Example 1 Find the Slope of a Line
Find the slope of the line passing through and .
( )51,–( )23,
5–2–3 ( )1–= Substitute values.
, or43–
43–= Simplify.
SOLUTION
=Let and . ( )x1, y1 ( )x2, y2( )51,– ( )23,=
Rise: Difference of y-valuesm =
–y2 y1
–x2 x1 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, y1 ( )x2, y2 ( )51,–( )23,=
Classify Lines Using SlopeExample 2
Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical.
( )14,– ( )1,– 2– ( )23, ( )53,a. b.
SOLUTION
a.33–
= 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 = 3–32–5 = 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,– 3–( ),23,
2. ( ),81,– ( )1,– 1–
ANSWER undefined slope; is vertical
Find and Use Slope
Checkpoint
3. ( ),45,– ( )41,–
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–
SOLUTIONLine 1 and Line 2 pass through the given points.
Slope of line 2: m2 =– 62
–4= ( )1– 5
4–
Slope of line 1: m1 =– 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.
m1 m2>
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.
SOLUTIONLet and .( )x1, y1 ( )0, 2100= ( )x2, y2 ( )30, 1800=
Average rate of change =Change in temperature
Change in time
–1800°F–30 min
=2100°F0 min
–30 min
=300°F
–= 10°F/min
Example 4 Slope as a Rate of Change
ANSWERThe average rate of change is per minute. On average, the lava cools 10 degrees Fahrenheit each minute.
–10°F
Checkpoint
6.
ANSWER6a. 9.6 million subscribers per yr
6b. 19.75 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 2006. Find the average yearly rate of change in the number of subscribers (a) from 1993 to 1998 and (b) from 1998 to 2006.
Slope as a Rate of Change