### Student Page 2.2.3 It's A Matter of Scale

How important are the scales chosen for both the horizontal and vertical axes to the appearance of a graph or a group of graphs? Think about this question as you work together on the following tasks.

Among groups, compare graphs for Student Page Exercise 2.2.3.3 and Task 2.2.3.4.a. What do you notice? Think about these questions:

Are all of the graphs the same shape?

Why did all of the graphs look the same in Student Page Exercise 2.2.3.3?

Why do the graphs look different in Task 2.2.3.4.a

Discuss the importance of scale.

Think about Location, Location, Location How important was scale in helping you determine the location of each place? Does the \(x\)-scale matter? Does the \(y\)-scale matter?

Directions: Each group member receives a card with an equation on it and both \(x\)- and \(y\)-scales to use to graph the equation. Cards are found in It's a Matter of Scale Card Set.

#### 1.

Starting with zero at the origin, the point where the axes intersect, each tick mark increases by the amount of the scale provided. Label both the \(x\)- and \(y\)-axes showing the scale on the card.

#### 2.

Create a table that fits the equation and \(x\)-scale you were given. Plot the points in the table on the coordinate grid. Graph the equation by connecting the points you found. Write the equation of the line on the graph you drew.

#### 3.

##### (a)

Compare the graphs drawn by members of your group and class. What do you notice?

##### (b)

Look carefully at the equations plotted and the scales used. Should the graphs appear as they do? Why or why not?

##### (c)

Explain why the graphs appear as they do.

#### 4.

Work with other members of your group.

##### (a)

Graph the equations each person was provided on the same graph using the largest \(x\)- and \(y\)-scales provided in the set of cards.

##### (b)

What do you notice?

##### (c)

Discuss any differences in the appearances of the graphs compared to the graphs plotted in Student Page Exercise 2.2.3.2.

##### (d)

Why do the graphs in Student Page Exercise 2.2.3.2 look different from the graphs in Task 2.2.3.4.a?

#### 5.

Write about the importance of scale in graphing.