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!

Warm Up Linear or Nonlinear If linear, write equation y = 1/4x Y = x – 1 y = 3x + 5

Write the equation that matches the graph Y = 8/3x + 4 y = -5/3x + 1

QUIZ Direct Variation Slope Look at a table 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 it’s linear or nonlinear Write an equation from it if it’s linear

Slope Why is it important, and when do we ever use this in real life?!?!?!

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?

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

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 You’re charged a fee of $32 just to rent the car

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

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

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

Graph the ordered pairs in the table on a coordinate plane Graph the ordered pairs in the table on a coordinate plane. Should you draw a line connecting the points?

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

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!

You Try! Penny’s savings On Penny’s 15th 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 she’ll have on her 18th birthday.

a) Fill in the table above with the missing number of quarters. b) Identify the independent and dependent variables. c) Does Penny’s 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 18th birthday

b) Identify the independent variable. Identify the dependent variable. Independent variable is the months; dependent variable is number of quarters c) Does Penny’s 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.

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 18th birthday. Penny would have 2012 quarters on her 18th birthday.

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

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.