Warm Up • You are driving a huge tractor trailer. You use up ½ a gallon per mile. How far if have you traveled if you use up 9.5 gallons of your tank? • What is the independent and dependent variable? • Write an equation for this scenario. Solve it.
Objective Determine more appropriate Linear models and know types of slope
Example 6 • You are really hungry. You just had a really long workout. You go to In and Out and you really want burgers, animal style. There are 330 calories per burger. Make a linear model representing this scenario. Graph it. 1.7 Function Notation
Example 7 • You weigh 175 pounds. With each animal burger you eat, you will gain 1 more pound. Write a function representing this situation. 1.7 Function Notation
Example 8 • Ms. Stine is having a quiz on Friday. You get 5 points for every correct question. Write a linear model representing this situation • If there are 21 questions, what is the maximum score you can get 1.7 Function Notation
Example 9 • It is midday and it is 90 degrees outside. Every hour, the temperature drops 5 degrees. Write a linear model representing this situation. • What domain makes sense? Range? • REASONable 1.7 Function Notation
Example 10 • Devin is unhappy that he does not have a girlfriend. He decides to go on 2 OKCupid dates a week. Make a linear model for this situation. What is a reasonable domain? Range? 1.7 Function Notation
Warm up Currently, Mount Kiliminjaro is 28,250 feet. Each year, the mountain erodes 100 feet. How long many years will it take for the mountain to be 25,000 feet tall? Write an equation that satisfies this scenario, then solve.
Inspirational Quote “Every strike is what brings you closer to the next home run.” -Babe Ruth
Objective • Define rate of change and apply it to real-life scenarios
Rate of change • Slope of a line • “Steepness” of line • Expressed in 2 units, mph, wpm, etc.
Gone skiing A lot of effort = positive slope Negative effort = negative slope
Zero Slope No incline= Zero slope
No Slope or Undefined Slope • You will fall off the cliff, there is NO SLOPE
Undefined slope (continued) Is this a function? Why or why not? Why does it have NO slope rather than 0?
Slope • Slope = Rise/Run Change in y Change in x
Example 1 • In 1990 Billy ran a 5 minute mile. By 1994 it had lowered to a 3.5 minute mile. Which of the following expresses the rate of change in his minute time per year from 1990 to 1994? • Graph the scenario.
Example 2 • Kenny’s savings account balance changed from $1140 in January to $1450 in April. Find the average rate of change per month. Round your answer to the nearest dollar. • Graph the scenario
Example 3 • Ms. Stine is on a hike. After 2 hours she is at an altitude of 400 feet. After 6 hours, she is at an altitude of 700 feet. • What is the average rate of change? • Graph the scenario
Example 4 • A plane left Chicago at 8:00 A.M. At 1: P.M., the plane landed in Los Angeles, which is 1500 miles away. What was the average speed of the plane for the trip? • Graph it!
Example 5 • After 30 baseball games (before doping), A-Rod had 25 hits. If after 100 games he had 80 hits, what is his average hits per baseball game?
Homework • Happy Wednesday!!