standard_description: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
problem_activity: Problem 1
What is an equation of the line represented in the graph below?
[IMG]
Problem 2
Four lines were used to define the edges of the trapezoid shown below.
[IMG]
Write an equation for each line described below.
a.   Line that passes through points
$$A$$
and
$$B$$
b.   Line that passes through points
$$B$$
and
$$C$$
c.   Line that passes through points
$$C$$
and
$$D$$
d.   Line that passes through points
$$D$$
and
$$A$$
Problem 3
Optional: Play the memory
Matching Game
with linear equations and graphs. Note that this requires some advance preparation.
Directions for students:
Find a partner and clear off your desks.
Separate the cards into a pile with equations and a pile with graphs.
Turn the equation cards over and organize them into rows/columns on one desk.
Turn the graph cards over and organize them into rows/columns on another desk.
On the first person’s turn, turn over an equation card and a graph card. If the cards match, then the player gets to keep the cards. If they do not match, turn the cards over in the same spot. The turn is over.
NOTE: If the player believes she or he has a match, then the player must prove that there is a match. The other player has the option to disagree and explain why. If the other player is right (and the first player was mistaken), then the other player gets to keep the card and then take a turn.
Repeat step 5 for the second player’s turn.
The game is over when all cards have been matched. The person with the most number of pairs wins the round. Another round may be played.


aligns: no