Alg1 Lesson 1.2: Recognizing Direct Variation

​Lesson 1.2: Recognizing Direct Variation

​Obj: I can formulate and solve problems involving direct variation.

EQ: How do I know if a scenario represents a direct variation?

Important Info:
A linear relationship has a constant rate of change, which can be visualized as the slope of the associated graph.
A linear direct variation can be expressed in the algebraic form y = kx, where k is a non-zero constant.

Part 1: Exploring the Relationship Between Side and Diagonal Length in Squares

Measure each square side and diagonal in millimeters (one tic mark on cm side).

1.2a: Use a ruler

Multiple Choice

Look at two square with different side lengths. Are the two diagonals the same length?

• No, since they have different side lengths.

• Sometimes, since they have different side lengths.

• Yes, since they have different side lengths.

Multiple Choice

What do you think a graph of this relationship would look like?

• a line

• a curve

• a weak scatterplot

Write a rule to determine the length of the diagonal based on the length of the side.

Sketch a Graph

For the side lengths and the corresponding diagonal lengths.

Create a Table of Values

In Your Journal...

Share your table, graph, and rule with a partner.

Come up with a formal algebraic rule to represent the relation between a square's side and diagonal lengths.

This is an example of direct variation

Pythagorean Thm

The measure of one quantity can be thought of as a multiple of the other.

Reasoning

Fill in the Blanks

If the side length of a square is 0, then the diagonal length is?

Part 2: Recognizing and Defining Direct Variation

How can we tell that each of these represents direct variation?

Look back at your table, graph, and formula for the square lengths

In Your Journal...

Direct Variation

Two quantities vary directly if one of them is a constant multiple of the other or if the quotient of the two quantities is constant. If quantities x and y vary directly, then they can be related by y = kx for some nonzero constant k.

How can you determine whether the temperature in degrees Celsius and the temperature in degrees Fahrenheit vary directly?

It is known that 0ºC is 32ºF and 100ºC is 212ºF.
It is encouraged to construct a table and/or graph.
Use the following words when explaining: constant of proportionality, input, output, and direct variation.

In Your Journal...

Categorize

Options (9)

The perimeter, P, of a square side length is n.

The area, A, of a square whose side length is n.

You are traveling on a bus to camp at a speed of 50 mph. The number of miles traveled, N, after

200 miles away at 50 mph. The number of miles, N, you have left to travel after t hours.

One pound costs $3.25. Five pounds cost $16.25.

y = 5x - 9

y = -2.4x

Sort each problem as direct or not

Direct Variation

Not Direct Variation

Part 3: Creating a Direct Variation Graphic Organizer

Fill out the graphic organizer in your journal for direct variation.

Frayer Model

Choose a skill TEKS to focus on, get that foldable and 1 WS from the folders on wall. Go to Canvas to click skill links.

Look at Calendar Paper

Share your thoughts with others around you!

Spin Wheel Discuss Question