Page 293 - Algebra 1

A rate of change is a ratio that compares the change in one quantity with the change in another. The slope of a line represents a rate of change.
Application: Determining Rates of Change
Alyssa used the second hand of a clock to record the time it took a train to travel the distance from her house to a friend’s house. The second hand of the clock was at 12 seconds when she began timing and at 38 seconds when the train had traveled the one-quarter-mile distance to her friend’s house. What was the speed of the train in feet per second?
SOLUTION
Understand Alyssa is trying to calculate the speed of the train based on changes in both time and distance. The speed can be expressed as a ratio of the changes in each quantity. _ _
speed = change in distance change in time
Plan Represent the original distance and time as one point on a line and the final time and distance as the second point. Then find the slope of the line connecting these two points.
Example
5
Hint
Remind students that there are 5280 feet in
1 mile. So, a quarter mile is 1320 feet.
Solve Use the slope formula to find the speed. Labelthepoints. (x,y) (12,0)and(x,y) (38,1320).
m = y2 - y1 = 1320 - 0 __
x-x
_2 1 38 - 12
m = 1320 = 50.8 ft/s 26
Determine the slope of the line that contains the given points.
(Ex 1)
a. (−3, −4) and (3, 0) b. (−5, 8) and (5, 6) c. (0, 6) and (1, 12)
d. (−2, 7) and (2, −9)
Determine the slope of the line that contains the points shown in the table.
e.
(Ex 2)
Apply the slope formula. Simplify.
___ 50.8 ft · 1mile ·3600 s
Check
11 22
=34.6mph
The speed of 34.6 mph is reasonable for a train.
s 5280ft hour
Lesson Practice
Math Reasoning
Generalize What pattern do you notice in lines that have a positive slope? a negative slope?
x
y
-4
-27
-2
-13
0
1
278 Saxon Algebra 1