Take turns with your partner to match a graph with each set of matching cards. Eventually all the cards will be sorted into groups of four cards (an equation, situation, table, and graph).
For each match that you find, explain to your partner how you know it’s a match. Ask your partner if they agree with your thinking.
For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
What did you and your partner agree are the cards that match the equation on card 1?
Compare your answer:
Cards 1, 11, 20, 32
What did you and your partner agree are the cards that match the equation on card 2?
Compare your answer:
Cards 2, 16, 18, 25
What did you and your partner agree are the cards that match the equation on card 3?
Compare your answer:
Cards 3, 10, 21, 29
What did you and your partner agree are the cards that match the equation on card 4?
Compare your answer:
Cards 4, 9, 23, 30
What did you and your partner agree are the cards that match the equation on card 5?
Compare your answer:
Cards 5, 12, 22, 31
What did you and your partner agree are the cards that match the equation on card 6?
Compare your answer:
Cards 6, 15, 24, 26
What did you and your partner agree are the cards that match the equation on card 7?
Compare your answer:
Cards 7, 14, 19, 27
What did you and your partner agree are the cards that match the equation on card 8?
Compare your answer:
Cards 8, 13, 17, 28
Self Check
Additional Resources
Linear Equations and Their Representations
Linear equations can be written from situations, tables of values, and graphs.
Here is a linear situation:
Sadie pays $15 a month for ballet classes plus $5 each lesson she takes.
First, make a table of values to represent how much Sadie pays for the first 5 lessons.
Number of Lessons | 0 | 1 | 2 | 3 | 4 | 5 |
Total Cost | 15 | 20 | 25 | 30 | 35 | 40 |
Next, graph all of the points:
Looking at the slope and -intercepts of the table and graph, write an equation.
Step 1 - Identify the -intercept.
When , so the -intercept is 15.
Step 2 - Identify the slope.
Slope is the change in over the change in . For this table, the change in is 43 and the change in is 1.
The slope is 3.
Step 3 - Write the equation in slope-intercept form.
In the slope-intercept form, , is the slope and is the -intercept.
The equation is .
Try it
Try It: Linear Equations and Their Representations
Write an equation from the table:
0 | 1 | 2 | 3 | 4 | |
7 | 11 | 15 | 19 | 23 |
Compare your answer:
Here is how to write an equation from a table.
Step 1 - Identify the -intercept.
When , so the -intercept is 7.
Step 2 - Identify the slope.
Slope is the change in over the change in . For this table, the change in is 4 and the change in is 1. The slope is 4.
Step 3 - Write the equation in slope-intercept form.
In the slope-intercept form, , is the slope and is the -intercept.
The equation is .