WARM-UP Using the data from Rasheed Wallace and Carlos Arroyo, find the equation for the line of best fit for this data set.

INTERPRETING SLOPE AND Y-INTERCEPTS Objective SWBAT interpret the slope and the intercept of a linear model in the context of the data. 3.1.c.i (CCSS: S-ID.7) DOL Given 3 CR questions, SW interpret the slope and intercept of a linear model in the context of the data with 80% accuracy. Essential Question What does each part of a function tell us?

QUICK REVIEW

Y-INTERCEPT y-intercept : The point where the graph crosses the y- axis This point represents the value of y when x is 0 This is often the starting point of a scenario

QUICK CHECK Find the y-intercepts of the following graphs (x, y) A BC (0, 2) (0, -1)(0, 0)

SLOPE Slope : the change in y over the change in x Slope tells the relationship between the independent and dependent variables—how much y goes up or down when x goes up Also known as rate of change

QUICK CHECK Find the slope of the following graphs A BC 3 -2½

QUICK CHECK What does the rate of change tell us in the following graph? The rate of change tells us how many dollars per day Billy Bob has

QUICK CHECK What does the rate of change tell us in the following graphs? The rate of change tells us how many miles per minute Mary Sue runs miles The rate of change tells us the cost per song

SLOPE-INTERCEPT FORM

INTERPRETING SLOPE AND Y-INTERCEPTS

DOMINO’S THROWBACK Number of Toppings Cost of Pizza

DOMINO’S THROWBACK Number of Toppings Cost of Pizza

IT’S FEELING COLDER…

DOWN FALLS THE RAIN City Elevation (feet) Average Precipitation (inches) Stockholm, Sweden17121 Berlin, Germany19023 London, England20330 Paris, France*21326 Bucharest, Romania*29823 Budapest, Hungary Toronto, Canada56731

DOWN FALLS THE RAIN City Elevation (feet) Average Precipitation (inches) Stockholm, Sweden17121 Berlin, Germany19023 London, England20330 Paris, France*21326 Bucharest, Romania*29823 Budapest, Hungary Toronto, Canada56731

DOWN FALLS THE RAIN City Elevation (feet) Average Precipitation (inches) Stockholm, Sweden17121 Berlin, Germany19023 London, England20330 Paris, France*21326 Bucharest, Romania*29823 Budapest, Hungary Toronto, Canada56731

DOWN FALLS THE RAIN City Elevation (feet) Average Precipitation (inches) Stockholm, Sweden17121 Berlin, Germany19023 London, England20330 Paris, France*21326 Bucharest, Romania*29823 Budapest, Hungary Toronto, Canada56731 less

DOWN FALLS THE RAIN City Elevation (feet) Average Precipitation (inches) Stockholm, Sweden17121 Berlin, Germany19023 London, England20330 Paris, France*21326 Bucharest, Romania*29823 Budapest, Hungary Toronto, Canada56731

UNEMPLOYMENT BASED ON EDUCATION The following data represents the unemployment rate in 2013 based on level of education No high school diploma High school diploma Some college Associate’s Degree Bachelor’s Degree More Degrees Highest Level of Education Level Unem- ployment Rate No diploma011.0% High school diploma17.5% Some college27.0% Associate’s degree35.4% Bachelor’s degree44.0% More degrees5 2.9%

UNEMPLOYMENT BASED ON EDUCATION The following data represents the unemployment rate in 2013 based on level of education Highest Level of Education Level Unem- ployment Rate No diploma011.0% High school diploma17.5% Some college27.0% Associate’s degree35.4% Bachelor’s degree44.0% More degrees5 2.9% A.Using the data from some college and bachelor’s degree, find the equation for the line of best fit. B.What does the y- intercept tell us in this scenario? C.What does the slope tell us in this scenario?

UNEMPLOYMENT BASED ON EDUCATION The following data represents the unemployment rate in 2013 based on level of education Highest Level of Education Level Unem- ployment Rate No diploma011.0% High school diploma17.5% Some college27.0% Associate’s degree35.4% Bachelor’s degree44.0% More degrees5 2.9%

UNEMPLOYMENT BASED ON EDUCATION The following data represents the unemployment rate in 2013 based on level of education Highest Level of Education Level Unem- ployment Rate No diploma011.0% High school diploma17.5% Some college27.0% Associate’s degree35.4% Bachelor’s degree44.0% More degrees5 2.9% What does the y-intercept tell us in this scenario? The y-intercept tells us that people without a high school diploma will have about a 10% unemployment rate. What does the slope tell us in this scenario? The slope tells us that the unemployment rate should decrease by about 1.5 percentage points for each level of education we add.

INCARCERATION BASED ON EDUCATION The following data represents the incarceration rate in based on level of education No high school diploma High school diploma Some college Associate’s Degree Bachelor’s Degree More Degrees Highest Level of Education Level Incarcera- tion Rate No diploma09.4% High school diploma12.8% Some college21.1% Bachelor’s degree40.2% A high school dropout is 47 times more likely to go to prison than a college graduate.

INCOME BASED ON EDUCATION The following data represents the average income of an individual in 2013 based on their level of education No high school diploma High school diploma Some college Associate’s Degree Bachelor’s Degree More Degrees Highest Level of Education Level Average Annual Income No diploma0$24,544 High school diploma1$33,852 Some college2$37,804 Associate’s degree3$40,404 Bachelor’s degree4$57,616 More degrees5 $79,508

INCOME BASED ON EDUCATION The following data represents the average income of an individual in 2013 based on their level of education Highest Level of Education Level Average Annual Income No diploma0$24,544 High school diploma1$33,852 Some college2$37,804 Associate’s degree3$40,404 Bachelor’s degree4$57,616 More degrees5 $79,508 A.Using the data from no diploma and a bachelor’s degree, find the equation for the line of best fit. B.What does the y-intercept tell us in this scenario? C.What does the slope tell us in this scenario? Extension: If you work for 40 years… How much more will you earn for each extra level of education you have? How much more would you make if you earn a college degree compared to someone who had no diploma?

INCOME BASED ON EDUCATION The following data represents the average income of an individual in 2013 based on their level of education Highest Level of Education Level Average Annual Income No diploma0$24,544 High school diploma1$33,852 Some college2$37,804 Associate’s degree3$40,404 Bachelor’s degree4$57,616 More degrees5 $79,508

INCOME BASED ON EDUCATION The following data represents the average income of an individual in 2013 based on their level of education Highest Level of Education Level Average Annual Income No diploma0$24,544 High school diploma1$33,852 Some college2$37,804 Associate’s degree3$40,404 Bachelor’s degree4$57,616 More degrees5 $79,508 What does the y-intercept tell us in this scenario? The y-intercept tells us that the average person with no diploma earned $24,544 in What does the slope tell us in this scenario? The slope tells us that you can expect to earn an extra $8,268 per year for each level of education you add.

INCOME BASED ON EDUCATION The following data represents the average income of an individual in 2013 based on their level of education Highest Level of Education Level Average Annual Income No diploma0$24,544 High school diploma1$33,852 Some college2$37,804 Associate’s degree3$40,404 Bachelor’s degree4$57,616 More degrees5 $79,508 Extension #1 If you work for 40 years, you can expect to earn more an extra $330,000 for every level of education you add. Extension #2 If they both work for 40 years, someone with a bachelor’s degree can expect to earn over $1.3 million more than someone without a high school diploma.

INCOME BASED ON EDUCATION The following data represents the average income of an individual in 2013 based on their level of education Highest Level of Education Level Average Annual Income No diploma0$24,544 High school diploma1$33,852 Some college2$37,804 Associate’s degree3$40,404 Bachelor’s degree4$57,616 More degrees5 $79,508

DATA SUMMARY If you graduate from high school… You’ll make about $9,000 more per year, which adds up to over $350,000 in 40 years You’re about 32% less likely to be unemployed You’re 3 times more likely to stay out of prison compared to someone who doesn’t graduate from high school If you graduate from college with a bachelor’s degree… You’ll make about $33,072 more per year, which adds up to over $1.3 million in 40 years You’re about 64% less likely to be unemployed You’re 47 times more likely to stay out of prison compared to someone who doesn’t graduate from high school

THE POWER OF HOMEWORK

MATH AND MAKING IT The following data represents the relationship between math and educational attainment Highest Level of Math in High School Level Odds of Earning a College Degree Pre-Algebra04% Math I / Math II113% Math III234% Pre-calculus355% Calculus4 73% Some college Pre-Algebra Math I / Math II Math III Pre-Calculus Calculus

MATH AND MAKING IT The following data represents the relationship between math and educational attainment Highest Level of Math in High School Level Odds of Earning a College Degree Pre-Algebra04% Math I / Math II113% Math III234% Pre-calculus355% Calculus4 73% A.Using the data from Math I / Math II and Calculus, calculate the line of best fit for the data. B.What does the y- intercept tell us in this scenario? C.What does the slope tell us in this scenario?

MATH AND MAKING IT The following data represents the relationship between math and educational attainment Highest Level of Math in High School Level Odds of Earning a College Degree Pre-Algebra04% Math I / Math II113% Math III234% Pre-calculus355% Calculus4 73%

MATH AND MAKING IT The following data represents the relationship between math and educational attainment Highest Level of Math in High School Level Odds of Earning a College Degree Pre-Algebra04% Math I / Math II113% Math III234% Pre-calculus355% Calculus4 73% What does the y-intercept tell us in this scenario? The y-intercept that someone who has zero years of high school math have a –27% chance of graduating from college. Does this y-intercept make sense? No, it’s impossible for someone to have a negative chance of graduating from college. The line of best fit gives us a prediction, but it isn’t perfect.

MATH AND MAKING IT The following data represents the relationship between math and educational attainment Highest Level of Math in High School Level Odds of Earning a College Degree Pre-Algebra04% Math I / Math II113% Math III234% Pre-calculus355% Calculus4 73% What does the slope tell us in this scenario? The slope tells us that we’re 20% points more likely to graduate from college for each additional level of high school math we complete.

DOL #1 The following table shows the relationship between Sandra’s time exercising and the number of calories she burns. A.What does the y-intercept tell us in this situation? B.Pick two points to calculate the slope. What does the slope tell us in this situation? When Sandra exercises for zero minutes, she burns zero calories. The slope is between 2.5 and 7.4 and it tells us how many calories Sandra burns per minute.

DOL #2 The following graph represents the amount of strawberries picked per hour throughout a day. A.Find the line of best fit using the points (1, 73) and (8, 41). B.What does the y-intercept tell us in this situation? C.What does the slope tell us in this situation?

DOL #2 ANSWERS The following graph represents the amount of strawberries picked per hour throughout a day.

DOL #2 ANSWERS The following graph represents the amount of strawberries picked per hour throughout a day. What does the y-intercept tell us? The y-intercept tells us that we start the day picking strawberries at a rate of 78 quarts per hour. What does the slope tell us? We pick slower throughout the day at a rate of 4.6 fewer quarts per hour.