Ratios and Proportionality

Ratios and Proportionality

by Joshua Polk

Constant Proportionality (k)

Multiple Choice

Do the matching table and graph represent a proportional relationship?

• Yes, they represent a proportional relationship.

• No, they do not represent a proportional relationship.

Multiple Choice

Do the matching table and graph represent a proportional relationship?

• Yes

• No

How to spot k CONSTANT PROPORTIONALITY

• Unit Rate (each, every, per, a)

• Examples: 55 miles per hour, $4.25 per pound, 0.1 kilometer per minute

• A constant rate - $30 for 5 hours, $32 every 4 months

How to FIND k (constant proportionality)

• If given a UNIT RATE (55 miles per hour) K equals the number you are multiplying by. k = 55

• y = 55x

Multiple Choice

k represents

• the constant of proportionality

• the king

• ketchup

• a strikeout

Multiple Choice

Which equation matches the constant of proportionality?

• x = y

• y = x

• y = kx

• l x w

Multiple Choice

Identify the constant of proportionality.

• k = 2x

• k = 2

• k = 4

• none (not proportional)

Multiple Choice

The constant of proportionality in the equation y = ½x is _______. 

• x
• y
• 1/2
• 2

Multiple Choice

The constant of proportionality can be found by finding the ______ ______.

• unit rate

• ratio rate

• proportion answer

• rational number

How to FIND k (constant proportionality)

• If given a constant rate ($30 for 5 hours) use 

• y = 6x, Olivia is paid $6 per hour for babysitting. The equation will find how much she will be paid for x amount of hours

How to FIND k (constant of proportionality)

Multiple Choice

Which equation helps you solve for k?

• $$k\ =\ \frac{x}{y}$$

• $$k\ =\ \frac{y}{x}$$

• k = y + x

• k = 2x

Multiple Choice

What is the constant of proportionality for this table?

• $1/9 per hour

• $9 per hour

• $8 per hour

Multiple Choice

Write the equation for the table given.

• y = 16x

• y=8x

• y=12x

Multiple Choice

Determine the missing value in the table.

• 15

• 3

• 1/3

• 9

Multiple Choice

What is the constant of proportionality?

• 15

• 3

• 1/3

• 9

Today we will interpret what data points mean on a graph depicting a proportional relationship.

Tyler was at the amusement park. He walked at a steady pace from the ticket booth to the bumper cars.

• The point on the graph shows his arrival at the bumper cars.

• What do the coordinates of the point tell us about the situation?

Open Ended

What do the coordinates (40,50) tell us about the situation?

The point (40,50) tells us that 40 seconds after Tyler started walking, he was 50 meters from the ticket booth.

• .

Open Ended

What do the coordinates (0,0) tell us about the situation?

The point (0,0) tells us that Before any time passed, there was no distance between Tyler and the ticket booth.

• .

The table representing Tyler's walk shows other values of time and distance.

• Find the constant of proportionality.

• Then, decide what the missing value would be.

Open Ended

What value should be added to the blank spot on the table?

Tyler was 1.25 meters from the ticket booth after 1 second.

• The corresponding point is (1, 1.25)

• The constant of proportionality is 1.25. It tells us that Tyler is walking at a speed of 1.25 meters per second. It appears as the second coordinate in

Open Ended

If the constant is 1.25 what is the equation of the line. (y=kx)

One Last Question

2 Parts

The graph shows the amounts of almonds, in grams, for different amounts of oats, in cups, in a granola mix.

• You will need to identify the value of k in the point (1,k) .

• Then interpret the meaning of it the coordinate point.

Multiple Choice

Part 1: Identify the value of k in the point (1,k) .

• 1

• 20

• 25

• 30

Open Ended

Part 2: What does the point (1,25) mean?

Multiple Choice

What is k in this proportional relationship?

• 60

• 120

• 1

• 180

Multiple Choice

What is the constant of proportionality for the following graph?

• 80

• 20

• 40

• 160

Multiple Choice

Which statement matches the graph?

• Taylor can write 6 words per minute

• Taylor can write 25 words per minute

• Taylor can write 50 words per minute

• Taylor can write 150 words per minute

Great work today!