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 2 Exploring Linear Relationships with Graphs and tables.

Homework Pg 38 Assigned 12/9 Due 12/12 A 2, 3 b - e, 4, 7, 8, 17 B 6, 9, 10, 17, 45 IXL Assigned 12/9 Due 12/13 F 6 compare and order fractions X 18 Similar triangles and indirect measurement

INVEST 2. 1 AND 2. 2 FINDING POINTS OF INTERSECTION USING A TABLE, GRAPH OR EQUATION Students will compare two sets of data using tables graphs and equations. Students will identify the point of intersection and describe what it means.

Example In Ms. Chang’s class, Emile found out that his walking rate is 2. 5 meters per second. When he gets home from school, he times his little brother Henri. He figures out that Henri’s walking rate is 1 meter per second. Henri challenges Emilee to a walking race. Because Emile’s walking rate is faster, he gives Henri a 45 meter-head start. 1. Make a table for Henri and Emile 2. Graph both sets of data 3. Write the equation for Henri and Emile 4. How long should the race be so that Henri will win in a close race? 5. Which method worked the best to help determine how long to make the race so it was close and Emile still wins?

6. Continuing Emile’s and Henri’s race How does the walking rate show up in each method? 7. How far does Emile walk in 20 seconds? 8. After 20 seconds how far apart are the brothers? How is this distance represented in all 3? 9. Is the points (26, 70) on either graph? 10. When will Emile overtake Henri? 11. Can you determine which line is steeper, all methods? 12. At what point do the lines cross the y-axis, how can you determine this in all methods? 13. Can you determine where the lines intersect, all methods?

Graph? How to solve a problem NOTES Can look at a picture of the data, seeing more of the points, not always easy to tell what points Can see point of intersection to interpret questions Steepness of line, how fast it goes up or down from Left to Right Can see the y intercept Table? rate You can look at the data side by side, but don’t see all the data points, can determine pattern Look at pattern to determine steepness Can determine the y-intercept when x = 0 Equation? Best when comparing rates, y-int, and finding values You can see the slope or rate of each line You can see the y-intercepts or

NOTES Intersection point of 2 lines To the left one line is better why Intersection both are the same To the right other line is better why Steeper Larger the rate the steeper the line, closer to vertical How fast the line goes up or down from left to right

Other things to remember to help with HW Equation of a line is y = mx + b M is the pattern in a table, or rate, slope of line which is y/x B is the y-intercept, where line crosses the y axis, when x = 0, starting point of graph You should be able to find these given anything and then sub them in correctly Profit = income - cost

INVEST 2. 3 COMPARING RELATIONSHIPS Students will be able to compare equations and tables to determine the type of relationship that is present?

Equation of a line Y=mx+b y is the dependent variable m is the slope, rate, always y/x x in the independent variable b is the y-intercept, point where graph starts where line crosses y-axis (0, b) (NOTES)

Example Warm-up on Orange sheet Ms. Chang’s class decides to give T-shirts to each person who participates in the walkathon. They receive bids for the cost of the T-shirts from two different companies. Mighty Tee charges $49 plus $1 per T-shirt. No Shrink Tee charges $4. 50 per T-shirt. 1. What is the equation for each company? 2. State the y-intercept and rate for each company, what do these mean 3. For each company what is the cost for 12 shirts? 20 shirts? 4. Lani calculates that the school has about $120 to spend on T-shirts. From which company could they buy the most? 5. For what number of T-shirts is the cost of the two companies the same, how did you determine this, what does this point mean

Problem 2. 3 B The following table represents the cost from another company 1. Is this linear? Is it a proportional relationship? How did you determine this What is the rate or slope for this company? 2. Write an equation for this plan 3. Graph it on the same coordinate plane as the other two 4. How does this compare to the other companies? 5. Would the point (20, 84) be on this cost plan? Explain

INVEST 2. 4 CONNECTING EQUATIONS, TABLES AND GRAPHS Students will determine solutions to problems using equations, tables and graphs.

Notes How does the equation, table and graph represent the following, how are the answers displayed Positive Slope Goes up from left to right Negative Slope Goes down from left to right Slope of 0 Horizontal Line y=# Start example on orange sheet, make tables for all 3 from -5 to 5

Example Consider the following pledge plans. In each equation, y is the amount pledged in dollars by each sponsor, and x is the distance walked in kilometers. 1. Make a table from -5 to 5 and graph each equation 2. Graph each plan 3. List information given from each of the methods

What you should notice Equation the rate of the line the y-intercept Table y values go up down or constant Graph line goes up down or constant y-intercept

Discuss HW and Quiz HW 2 – similar to what was done in class Wed 3 – similar to 2, reading a graph 4 – linear, eq amd explain 8 – point of intersection 17 – matching graph and equation 6 – reading a graph profit = income- expense 9 – 3 situations 10 – intersection

Quiz 4 questions 2 to 3 parts each still 20 points Similar to homework problems Looking at comparing 2 linear equations

Things you can work on 1. Fix homework due 2. Corrections on wkst due Mon 3. Essential questions for Invest 2 4. Study for quiz, do other hw problems 5. IXL due Frid 6. IXL from last week up to 100 due Sunday and email me