MOVING STRAIGHT AHEAD Students will work on linear

MOVING STRAIGHT AHEAD Students will work on linear equations, solving inequalities, determining slopes and what they mean, and determining the intersection of 2 lines.

INVESTIGATION 1 In this unit students will review unit rates and relate them to linear relationships.

Homework Page 16 Assigned 12/2 Due 12/5 A 1, 4, 6, 10, 12, 13 B 7, 10, 11, 12, 14, 31 IXL this will be review material for the final Assigned 12/2 Due 12/6 C 9 adding and subtraction C 20 multiplying and dividing

INVEST 1. 1 Students will be able to use a rate to determine a relationship between distance and time? Students will be able to determine what the independent and dependent variables are based on the rate.

Lab – determine your walking rate Each square in the hallway is 12 inches Mark off 30 feet, how many yards is this Do problem 1. 1 on page 9 – we are using Feet instead of meters Do this for 2 different people and at least twice for each Use yards per second Answer questions on given sheet

Key Ideas Rate – distance over time This is also the constant of proportionality Graph would be a straight line starting at (0, 0), how do we know this y=kx this will change to y=mx+b, what does the b tell us M is the slope or rate in this case, does not need to be the unit rate, but it is a rate, be able to describe what the slope means, when will it be a unit rate m=change in y/change in x we will discuss more later Be able to write equation and know if you are subbing in value for x or y

INVEST 1. 2 Students will be able to determine the relationships between linear equations from tables and graphs? Students will be able to write a linear equation given a table or graph by using rates?

Problem 1. 2 Using the cut out for your notes 1. Complete the table for the three students, how does the walking rate appear as a pattern 2. Graph all three on the same graph, how do you notice the walking rate on the graph 3. Write an equation for each, how do you notice the rate in the equation 4. How could you determine the graph would be a straight line from the table? Equation? 5. Are any of these proportional relationships? How do you know? If yes what is the constant of proportionality?

Problem 1. 2 B For each student 1. If time t increase by 1 second, by how much does the distance d change? 1. 2. If t increase by 5 seconds, by how much does d change? 1. 3. How did you determine this? How is the change represented in a table? Graph? How did you determine this? What is the walking rate per minute? Per hour?

Key Ideas Rate again is the y/x Graph it goes up in a straight line, you can always see the same triangle between points Table pattern of the y’s is the same Equation the number in front of the x Proportional Relationships graph has to go through (0, 0) Table has to have (0, 0) equation has no b value

Graphing a linear relationship 1. Make a table starting when x=0 and continue for at least 4 more numbers 2. Calculate the y value – continually add the unit rate 3. Plot the points on a graph For graph – make sure you have axis labeled, make sure you have a good scale for x and y axis

Example is the relationship linear, explain

INVEST 1. 3 Students will be able to determine dependent and independent variables based on the rate?

Problem 1. 3 Complete the handout Table and Graph What is the dependent variable? What is the independent variable? What are the equations for each?

Problem 1. 3 1. Suppose each student walks 8 km. 1. 2. Suppose each student raises $10 from a sponsor. 1. 3. How much money does each sponsor donates? Explain How many k does each student walk? Explain On which graph does the point (12, 11) lie? 1. What information does this point represent

Problem 1. 3 C Gilberto decides to give a T-shirt to each of his sponsors. Each shirt costs him $4. 75. He plans to pay for each shirt with some fo the money her raises from each sponsor. 1. Write an equation that represents the amount of money Gilberto raises from each sponsor after he has paid for the T-shirt. Explain what information each number and variable represents. 2. Graph the equation from distances from 0 to 5 km. Compare this graph to the graph of Gilberto’s pledge plan. 3. Is this relationship linear? Is it proportionally linear? Explain

Writing an equation Reviewing some Ideas Y=kx This is the proportional equation, where you start at (0, 0) What if you didn’t start at (0, 0) what does that do to the equation Y=mx+b M is the slope, rate of change, what is the value that you would constantly add or multiply by to get next value B do we start with something that won’t change, initial cost like charge to deliver a pizza no matter how many we order

Word Problems Can you write an equation, amount of money based on the number of kilometers walked? Is it linear? What is the b value in the equation y=mx+b

Answering questions based on table graph or equation How do you answer questions based on what is given? Table continue the table of data, what if x value is not part of data Graph continue graph and go up from x or y axis and find intersection Equation sub in given value into correct variable and solve All have pros and cons Equation most accurate, graph is the least

INVEST 1. 4 Students will be able to recognize a if a pattern of data is linear by finding and interpreting the pattern of the data.

Recognizing Information based on linear graph, table or equation Start of the problem y-intercept, the b value, when x=0 What is done per slope, m, rise/run, rate Equation y=mx+b Increasing m is positive, values go up over x value increasing, up from left to right Decreasing m is negative, values go down over x value increasing, down from left to right

Example 1. How much money is in the account at the start of the project? 2. How much money is withdrawn from the account each week? 3. Is this a proportional relationship? 4. Write an equation? 5. Is this linear? Explain

Problem 1. 4 B Mr. Mamer’s class also raised money from the walkathon. They use the money to buy games and puzzles for the children’s ward. Keenan uses a graph to keep track of the amount of money in the account at the end of each week. 1. What information does the graph represent? 2. Write and equation to represent the graph?