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Triangle XYZ has vertices X(2, 2), Y(10, 4), and Z(8, 10). Find the vertices of triangle XYZ after a dilation with a scale factor of 3.
Bell-work 9/28/15
A student is making a model skeleton of the human body. The scale she is using is 0.5 inch = 1 foot. Find the model length for the height that has an actual length of 12 feet.
Find a Positive Rate of Change
DOGS The table below shows the weight of a dog in pounds between 4 and 12 months old. Use the information in the table to find the rate of change in the dog’s weight between 8 and 12 months of age.
Find a Positive Rate of Change
Answer: The dog grew an average of 3.75 pounds per month.
The dog grew from 28 to 43 pounds from ages 8 to 12 months.
Subtract to find the change in weights and ages.
Express this rate as a unit rate.
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B. B
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A. 2 inches per year
B. 2.2 inches per year
C. 2.5 inches per year
D. 3 inches per year
HEIGHTS The table below shows Julia’s height in inches between the ages of 6 and 11. Find the rate of change in her height between ages 6 and 9.
Find a Negative Rate of Change
SCHOOLS The graph shows the number of students in the eighth grade between 2000 and 2004. Find the rate of change between 2002 and 2004.
Find a Negative Rate of Change
Use the data to write a rate comparing the change in students to the change in time.
The number of students changed from 485 to 459 from 2002 to 2004.
Simplify.
Express as a unit rate.
Find a Negative Rate of Change
Answer: The rate of change is –13 students per year. The rate is negative because between 2000 and 2002, the number of students decreased. This is shown on the graph by a line slanting downward from left to right.
• linear relationship
• constant rate of change
• Identify proportional and nonproportional linear relationships by finding a constant rate of change.
Identify Linear Relationships
BABYSITTING The amount a babysitter charges is shown. Is the relationship between the number of hours and the amount charged linear? If so, find the constant rate of change. If not, explain your reasoning.
Identify Linear Relationships
Examine the change in the number of hours worked and in the amount earned.
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BABYSITTING The amount a babysitter charges is shown. Is the relationship between the number of hours and the amount charged linear? If so, find the constant rate of change.
Find a Constant Rate of Change
TRAVEL Find the constant rate of change for the hours traveled and miles traveled. Interpret its meaning.
Choose any two points on the line and find the rate of change between them.
Find a Constant Rate of Change
Answer: The rate of speed is 30 miles per hour.
The amount of miles changed from 60 to 120 between hours 2 and 4.Subtract to find the change in miles and the change in time.
Express this rate as a unit rate.
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A. The rate of speed is20 miles per hour.
B. The rate of speed is 25 miles per hour.
C. The rate of speed is 40 miles per hour.
D. The rate of speed is 50 miles per hour.
TRAVEL Find the constant rate of change for the hours traveled and miles traveled. Interpret its meaning.
Identify Proportional Relationships
TAXIS Use the graph to determine if there is a proportional linear relationship between the miles driven and the charge for a ride. Explain your reasoning.
Since the graph of the data forms a line, the relationship between the two scales is linear. This can also be seen in the table of values created using the points on the graph.
Identify Proportional Relationships
To determine if the two scales are proportional, express the relationship between the charges for several miles as a ratio.
Answer: Since the ratios are not all the same, the total charge is not proportional to the number of miles driven.
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MOVIES Use the graph to determine if there is a proportional linear relationship between the number of movies rented and the total cost. Explain your reasoning.
A. The data lie in a straight line and the ratio of the number of movies rented to the total cost is always the same, so there is a proportional linear relationship.
B. The data lie in a straight line but the ratio of the number of movies rented to the total cost is not always the same, so there is not a proportional linear relationship.
