Moving Straight Ahead Students will work on linear equations, solving equations, solving inequalities, determining slopes and what they mean, and determining the intersection of 2 lines.

Exploring Linear Relationships with Graphs and tables. Investigation2 Exploring Linear Relationships with Graphs and tables.

Vocab Coefficeint Number in front of the variable Y-intercept Point where line crosses the y axis, when x=0, starting point X-intercept point where line crosses the x axis, when y=0 Solution Point that makes an equation turn, ordered pair Intersection Point where two lines cross, the one ordered pair that will make both equations true

Homework Pg 38 A 2, 3, 4, 7, 8, 17 B 6, 9, 10, 17, 42 Worksheet

When is it helpful to use a graph or a table to solve a problem? Invest 2.1 and 2.2 Finding Points of Intersection Using a table, graph or equation When is it helpful to use a graph or a table to solve a problem? How does the pattern of change for a linear relationship appear in a table, a graph, or an equation?

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. Make a table for each Graph both tables Write the equation for both How long should the race be so that Henri will win in a close race? Which method worked the best?

Continuing Emile’s and Henri’s race How does the walking rate show up in each method? How far does Emile walk in 20 seconds? After 20 seconds how far apart are the brothers? How is this distance represented in all 3? Is the points (26,70) on either graph? When will Emile overtake Henri? Can you determine which line is steeper, all methods? Can you determine where the lines intersect, all methods?

How to solve a problem NOTES Graph? 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 Table? You can look at the data side by side, but don’t see all the data points, can determine pattern or rate Equation? Best when comparing rates, y-int, and finding values

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

Invest 2.3 Comparing Relationships How can you decide if a table or an equation represents a linear relationship?

Equation of a line (NOTES) Y = m x + b y is the dependant variable m is the slope, rate x in the independent variable b is the y-intercept, point where graph starts

Example 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. What is the equation for each company? State the y-intercept and rate for each company For each company what is the cost for 12 shirts? 20 shirts? Lani calculates that the school has about $120 to spend on T-shirts. From which company could they buy the most? For what number of T-shirts is the cost of the two companies the same

Invest 2.4 Connecting equations, tables and graphs How are solutions of an equation of the form y=mx+b related to the graph and table for the same relationship?

Example Consider the following pledge plans. In each equations, y is the amount pledged in dollars by each sponsor, and x is the distance walked in kilometers. Make a table from -5 to 5 and graph each equation What do you notice about each graph

Notes Positive Slope Goes up from left to right Negative Slope Goes down from left to right Slope of 0 Horizontal Line y=#