how do you know what 1400 and -350 mean in the context of the scenario?
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How do you know what 1400 and -350 mean in the context of the scenario?. A pool is being emptied. The equation to model the remaining water (W) at time (t) is W = 1400 – 350t. - PowerPoint PPT PresentationTRANSCRIPT
How do you know what 1400 and -350 mean in the context of the scenario?
A pool is being emptied. The equation to model the remaining water (W) at time (t)
is W = 1400 – 350t
In this lesson you will learn how to interpret the rate of
change and the y-intercept in context by examining each of
the four representations.
Let’s ReviewLet’s Review
Rate of change (slope)
x (days late)
y (late fees)
1 $0.502 $1.003 $1.504 $2.00
= 0.50
1.00 – 0.502 - 1 0.501
Initial value (y-intercept)
= 0
Let’s ReviewA Common MistakeSuppose a car is traveling 35 miles per
hour. An equation could be D = 35h, where D is distance after h hours.
What does 35 mean within the context of the scenario?The car goes 35 miles.
Incorrect !The car travels 35 miles for
every hour that passes.
Let’s ReviewCore Lesson
A 1400 gallon pool is being emptied at a rate of 350 gallons per hour.
W = -350T + 1400
T (hours)
W (remaining
gallons)0 14001 10502 7003 350
100
Let’s ReviewCore LessonRate of change
(slope) =Initial value (y-
intercept) =-350 1400
Meaning: The pool is losing 350 gallons of water every hour.Meaning: The pool has 1400 gallons before it begins to drain.
In this lesson you have learned how to interpret the rate of
change and the y-intercept in context by examining each of
the four representations.
Let’s ReviewGuided Practice
A car rental agency charges $30 plus $0.25 per mile for each mile driven.
C = 30 + 0.25m
Identify the slope and y-intercept in each representation. Explain the meaning of each.
m (miles)
C (cost)
0 $304 $318 $3212 $33
Let’s ReviewExtension ActivitiesShow an image of a restaurant price board or menu. -Are the prices slopes or y-intercepts?-What does each mean as it pertains to the restaurant?-There is an unseen value for each of the prices, what is it (slope or y-intercept)?-What does the unseen value mean as it pertains to the restaurant?
Let’s ReviewExtension Activities
Think of a situation pertaining to your life that would have a slope and y-intercept.
Share the situation, slope, y-intercept, and meaning within the situation.
Let’s ReviewQuick Quiz
A restaurant charges $150 for a room and $10 per person for food and drinks. What is the slope and what does it mean in the context of the scenario?
a) Total increases $10 for the room cost.b) Total increases $10 for every added personc) Total is $150 for the room cost.d) Total is $150 for every added person.
Let’s ReviewQuick Quiz
A restaurant charges $150 for a room and $10 per person for food and drinks. What is the y-intercept and what does it mean in the context of the scenario?
a) Total is $10 with zero people attending.b) Total increases $10 for every added personc) Total is $150 with zero people attending.d) Total is $150 for every added person.