Warm Up Write down objective and homework in agenda Lay out
homework (Linear vs Nonlinear wkst) Homework (Making Sense of Slope
Worksheet) QUIZ TOMORROW! Get graph paper!
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Warm Up Linear or Nonlinear If linear, write equation y = 1/4x
Y = x 1 y = 3x + 5
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Write the equation that matches the graph Y = 8/3x + 4 y =
-5/3x + 1
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QUIZ Direct Variation Finding the constant of variation Writing
equations in direct variation (from an ordered pair and word
problem) Determine if the equation is a direct variation Find the
missing value Slope Find the slope of a line (graph and ordered
pairs) Find the slope and y intercept Slope intercept form Graph an
equation in slope intercept form Write an equation from a graph
Know how to move a line on a coordinate graph (up, down/steepness)
Look at a table Tell if its linear or nonlinear Write an equation
from it if its linear
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Slope Why is it important, and when do we ever use this in real
life?!?!?!
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Real World Meanings After calling a rental car company, you
learn that to rent a medium-sized car the cost would be $32 per day
plus $0.25 for each mile driven over 150 miles. The equation that
represents this situation is y = 0.25x + 32, where y represents the
total cost of renting a car and x represents the number of miles
driven over 150 miles. What is the real world meaning of the
slope?
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Real World Meanings Slope is a rate of change. You are always
comparing two things. Therefore, when explaining the real world
meaning, you have two factors involved Slope = vertical horizontal
Slope = y x Add the x & y labels Cost Mile $1 per every 4 miles
= 1 4
Slide 8
Real World Meaning The y intercept always tells us what you
have already, before any time passes. (Or whatever label is on the
y axis) (0, 32) It costs $32 to drive 0 miles Youre charged a fee
of $32 just to rent the car
Slide 9
Real World Meanings The graph of y = -1/25x + 15 is shown at
the right What does the slope represent in this situation? Answer:
Gallons used per mile. Real world meaning? You lose 1 gallon of gas
for every 25 miles you drive
Slide 10
Real World Meanings What does the y- intercept represent in
this situation? Answer: The amount of gasoline in the gas tank at 0
miles Real world meaning? Before you drive, right after you fill up
with gas, your car holds 15 gallons of gas
Slide 11
Real World Meaning The equation y =.10x + 500 can be used to
represent the salary of the salesman who earns a salary and
commission. (Commission is a percent of what someone sells) What is
the real world meaning of the slope? The y intercept? Slope: He
gets 10% of what he sells, or he gets $1 for every $10 he sells Y
intercept: He could sell nothing and still make $500. That is his
salary
Slide 12
Graph the ordered pairs in the table on a coordinate plane.
Should you draw a line connecting the points?
Slide 13
What is the equation, in slope intercept form, of the line? y =
-1500x + 25,000 What does the slope represent in the problem? You
lose $1500 in value for every 1 year What does the y intercept
represent? When the car is brand new, the cost is $25000
Slide 14
Using two different methods, find the value of the Wrangler in
2009 and 2014. Y = -1500(3) + 25000 2009: $20500 2014: $13000 From
the table in your calculator!
Slide 15
You Try! Pennys savings On Pennys 15 th birthday, her
grandmother gave her a larger jar of quarters. Penny decided to
continue to save quarters in the jar. Every few months she counts
her quarters and records the number a table like this one. Predict
how many quarters shell have on her 18 th birthday.
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a) Fill in the table above with the missing number of quarters.
b) Identify the independent and dependent variables. c) Does Pennys
saving of quarters appear to be a linear function of the number of
months she has saved? d) Graph the data. e) Find the slope of the
data and explain the real-world meaning of the slope as related to
the data described in the table. f) Write a NOW-NEXT rule to show
how the number of quarters Penny saves changes with each month she
saves. g) Write an equation of the form y = mx + b. h) What is the
real-world meaning of the y-intercept? i) Use your equation to
predict how many quarters Penny will have on her 18 th
birthday
Slide 17
b) Identify the independent variable. Identify the dependent
variable. Independent variable is the months; dependent variable is
number of quarters c) Does Pennys saving of quarters appear to be a
linear function of the number of months she has saved? Explain your
reasoning. Yes, the number of quarters seems to be going up in a
steady rate of change. d) Graph the data.
Slide 18
Answers e) Find the slope of the data and explain the
real-world meaning of the slope as related to the data described in
the table. The slope is 27; this means that each month, Penny
increases the number of quarters in her jar by 27. f) ) Write a
NOW-NEXT rule to show how the number of quarters Penny saves
changes with each month she saves. NEXT = Now + 27; starting at 158
g) Use the slope you found in 1d to write an equation of the form y
= mx + b. y = 27x + 158 h) What is the real-world meaning of the
y-intercept? There were 158 quarters in the jar when her
grandmother gave her the jar. i) Use your equation to predict how
many quarters Penny will have on her 18 th birthday. Penny would
have 2012 quarters on her 18 th birthday.
Slide 19
Create your own! Using the equation y = -4x + 100 Write your
own scenario. Include the real world meaning of the slope and y
intercept Make a table, and graph at least 5 points
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Answers 3. a) Graph I matches Boston Bank because it rises the
fastest. Graph II matches Consumers Bank because it rises at the
same rate as Atlantic Bank, but grater y-intercept. Graph III
matches Atlantic Bank because it rises at the same rate as
Consumers, but lower y-intercept. b) The Atlantic Bank pay rule A =
20 + 2n shows that workers there will be a base pay of $20 whether
or not they collect any credit card applications and an additional
$2 for each card application they collect.