TEKS 7.4A and 7.4C Review

TEKS 7.4A and 7.4C Review

7.4A represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt

7.4C determine the constant of proportionality (k = y/x) within mathematical and real-world problems

Vocabulary

Rate of Change is a rate that describes how one quantity changes in relation to another quantity (x and y). aka Unit Rate

Proportional Relationships are relationships between two quantities (x and y) in which the rate of change is constant.

Proportions says that two ratios (or fractions) are equal. 1/2 = 5/10

Calculating Rate of Change

Step 1: Write the rates in ratio form with y in the numerator and x in the denominator (y/x)

16/1 ; 32/2 ; 48/3 ; 64/4 ; 80/5

Step 2: Compare the rates (divide y by x). If they are equal, the relationship between both quantities is proportional.
- You can use the (horizontal, vertical or cross multiplication method to determine if relationships are proportional).

16/1 = 16 ; 48/3 = 16 therefore this is a proportional relationship.

Multiple Choice

Are the rates below proportional?

 $\frac{19\ dollars}{2\ lbs}\ \ \ \ \frac{76\ dollars}{8\ lbs}$  

• Yes. They both have a unit rate of $9.50/1 lb

• Yes. They both have a unit rate of $19/2 lbs. 

• No, they have different unit rates. 

Multiple Choice

Calculate the rate of change for the values in the table.

• No constant rate of change.

• $80 per month.

• $45 per month.

• $41 per month

Proportional Relationships in Equation Form

If a proportional relationship exists between two quantities (x and y), you can describe the relationship using the equation y=kx. Where y is equal to k times x.

The variable k is called the constant of proportionality, aka the rate of change, aka unit rate. k can be found by dividing y/x.

 $k\ =\ \frac{y}{x}$  

Writing Equations to represent Proportional Relationships

When given x and y values in table form, you are able to make an equation.

Step 1: Determine if the rates are proportional.

26/2 = 39/3. Proportional.

Step 2: If the rates are proportional determine k. (k = y/x)

26/2 = 13 ; 39/3 = 13; 78/6 = 13

k = 13

Step 3: Once you have determined k, write the equation.

y= 13x

Graphs of Proportional Relationships

Proportional relationship can be represented by in the form y = kx

Notice in the equation y = kx, if x equals 1, then y equals k. So, on the graph of a proportional relationship, when x equals 1, the corresponding y-value is the constant of proportionality.

Also, in the equation y = kx, notice if x equals 0, then y also equals 0. So, on a coordinate grid, the line is proportional if it goes through the origin (0,0).

In the graph, when x is 1, y is 10. k = 1.

Writing Equations to represent Proportional Relationships

When given x and y values in graph form, you are able to make an equation.

Step 1: Determine if the rates are proportional. Via ordered pairs. (Remember divide y by x)

(1,2) and (3,6) become 2/1 = 6/3. Proportional.

Step 2: If the rates are proportional determine k via ordered pairs (k = y/x)

2/1 = 2 ; 4/2 = 2; 6/3 = 2 ; k=2

Step 3: Once you have determined k, write the equation. (USE SUBSTITUTION TO CHECK YOURSELF)

y= 2x

Multiple Choice

What is the Constant of Proportionality for this table? Remember,

 $k\ =\ \frac{y}{x}$  

• k = 10

• k = 1

• k = 3

• k =1

Multiple Choice

Determine k in the graph shown.

• k = .50

• k = 2

• k = 1

• k = 1.5

YOUR TURN!!!

Work through the following problems overviewing

TEKS 7.4A & TEKS 7.4C

Multiple Choice

A dolphin travels through the water of a speed of 25 kilometers per hour. Which representation shows the distance a dolphin can travel at this rate?

• y = x + 25 ; where x represents the time in hours and y represents the distance in kilometers

• In 5 hours a dolphin can travel a distance of 135 kilometers.

Multiple Choice

A recipe says to use 3 cups of flour to make 48 cookies. The constant rate of proportionality that relates the number of cookies made, y, to the number of cups of flour used, x, is ______.

• 16

• 3/48

• 12

• 8

Multiple Choice

Cheddar cheese costs $4.25 per pound. Which equation best represents y, the total cost of x pounds of cheddar cheese?

• y = 4.25 + x

• x = 4.25y

• x = 4.25 + x

• y = 4.25x

Multiple Choice

Consider the equation y = kx where y = 7.5 and x = 3. What is the value of k, the constant of proportionality?

• 22.5

• 0.40

• 4.50

• 2.50

Multiple Choice

The table show's your profit from your summer mowing job. What is the rate of change?

• $10 per hour

• $5 per hour

• $15 per hour

• $20 per hour

Multiple Choice

Brooklyn is running a 5K. Her mom records her time at three places during the race as shown in the table. If Brooklyn runs at a constant rate per minute, which statement best describes the constant of proportionality?

• Brooklyn runs 2/3 kilometers per minute.

• Brooklyn runs 6 kilometers per minute.

• Brooklyn runs 1/6 kilometers per minute.

• Brooklyn runs 3/2 kilometers per minute.

Multiple Choice

As a school carnival, tickets can be purchased to participate in different activities. The table shows the total cost for different numbers of tickets. What is the constant of proportionality that relates, y the total cost in dollars to x, the number of tickets purchased?

• 4.00

• 0.25

• 1.00

• 0.10

Multiple Choice

The graph represents the linear relationship between the number of books Layla has read and the number of months she has been a member of a book club. Which verbal description best describes what is shown on the graph?

• Layla has read 3 books in the first 2 months she was a member of the book club.

• Layla has read 2 books in the first 3 months she was a member of the book club.

• Layla has read 4 books in the first 3 months she was a member of the book club.

• Layla has read 3 books in the first 4 months she was a member of the book club.

Multiple Choice

Frank and his family drove 6 hours every day during a road trip. Which graph best represents y, the total number of hours driver in x days?

Multiple Choice

If Justin can type 408 words in 4 minutes, how many words can he type per minute?

• 402 words per minute

• 100 words per minute

• 400 words per minute

• 102 words per minute

Multiple Choice

Caroline's cell phone plan costs $32 per month. Which table shows the sum of the amounts that Caroline will pay for her cell phone plan over the next 4 months?