Presentation on theme: "Unit 1 Modeling with Linear Equations"— Presentation transcript:
1 Unit 1 Modeling with Linear Equations Learning Goal: I can model real-life situations using linear equations
2 Warm-Up: Graph of the Day What are the y-intercepts for the yellow cab and the blue cab? What do these values represent.You miss the bus and need to take a cab 5km to school; which cab should you choose?If you wanted to travel as far as possible with $6, which cab should you choose?
3 Linear SystemsMany real-life situations can be modeled using linear equations.When 2 or more equations are used, it is called a system of equations. If all of the equations are linear, it’s called a linear system.
4 Linear SystemsThe solution to a linear system is an ordered pair that satisfies all equationsGraphically, the solution is the point where two lines intersect
5 Modeling with Linear Equations At the zoo gift shop, posters of polar bears are $1 and poster of penguins are $6. Charles spent $32 to buy 7 posters, how many of each did he buy?Let x represent the number of polar bear postersLet y represent the number of penguin postersYou were probably introduced to these kinds of problems in elementary school; they may have been called ‘guess and check’ problems or ‘trial and error’ problems. These problems can be represented with linear systemsDuring this unit, we will learn a more prescribed method for solving these problems (more accurate than guess and check). One of the most challenging aspects is constructing the equations based on a written description.Today we are going to practice constructing linear systems and not worry about solving the problem just yet.In these problems, there are usually 2 types of information (in this case # and cost). We need one equation for each type of info. Start by defining variables (use the question ‘how many’ as a guide) and use variable to come up with 2 equations (one for number and one for cost).
6 Modeling with Linear Equations Jamie went out to her grandfather's farm. Her grandfather has pigs and chickens on his farm. She noticed that there were a total of 26 heads and 68 feet among them. How many chickens and how many pigs did her grandfather have?What are the 2 pieces of information?Define variablesUse variables to make one equation for each type of information
7 Modeling with Linear Equations Yasmin has $8000 to invest and would like to earn $500 from the money. How much should she invest in a stock that has been paying 10% annual return and how much should she invest in savings bonds that pay 4% annual interest?What are the 2 pieces of information?Define variablesUse variables to make one equation for each type of information
8 Modeling with Linear Systems José travelled 95km from Oakville to Oshawa by car and GO train. The car averaged 60km/h, and the train averaged 90km/h. The whole trip took 1.5h. How long was he in the car? In the train?What are the 2 pieces of information?Define variablesUse variables to make one equation for each type of information
9 HomeworkPg # 7, 10, 19, 23, 26 Just define variables and write 2 equations; you don’t need to solve.