Matching Tables, Equations, and Graphs

1.13.3 Matching Tables, Equations, and Graphs

1.13.3 • Matching Tables, Equations, and Graphs

Activity

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

Which of the following is a representation of

y = 30x

$x$ 0 1 2 3

$y$ 30 35 40 45
Eric was paid $30 to cut grass in July plus $5 each time he came to cut the grass.
Josie paid $30 per pair of jeans.

$x$	0	1	2	3
$y$	30	35	40	45

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

This table displays the total cost associated with various numbers of lessons, from 0 to 5, showing a linear increase.

Next, graph all of the points:

A scatter plot with points at (0, 15), (1, 20), (2, 25), (3, 30), (4, 35), and (5, 40) showing a positive linear trend. The x-axis ranges from -1 to 7, and the y-axis ranges from -5 to 55.

Looking at the slope and $y$ -intercepts of the table and graph, write an equation.

Step 1 - Identify the $y$ -intercept.

When $x = 0$ , $y = 15$ so the $y$ -intercept is 15.

Step 2 - Identify the slope.

Slope is the change in $y$ over the change in $x$ . For this table, the change in $y$ is 43 and the change in $x$ is 1.

The slope is 3.

Step 3 - Write the equation in slope-intercept form.

In the slope-intercept form, $y = m x + b$ , $m$ is the slope and $b$ is the $y$ -intercept.

The equation is $y = 5 x + 15$ .

Try it

Linear Equations and Their Representations

Write an equation from the table:

$x$	0	1	2	3	4
$y$	7	11	15	19	23

This table presents five corresponding (x, y) data pairs, illustrating a linear relationship where y = 4x + 7.

Compare your answer:

Here is how to write an equation from a table.

Step 1 - Identify the $y$ -intercept.

When $x = 0$ , $y = 7$ so the $y$ -intercept is 7.

Step 2 - Identify the slope.

Slope is the change in $y$ over the change in $x$ . For this table, the change in $y$ is 4 and the change in $x$ is 1. The slope is 4.

Step 3 - Write the equation in slope-intercept form.

In the slope-intercept form, $y = m x + b$ , $m$ is the slope and $b$ is the $y$ -intercept.

The equation is $y = 4 x + 7$ .