A doctor collected data to determine the association between age of an infant and its weight. She modeled the equation y = 1.25x + 7 for the line of best fit. The independent variable, x, is time in months and the dependent variable, y, is weight in pounds. What does the slope mean in this context?

Question

Responses
A An infant's starting weight is 7 pounds.An infant's starting weight is 7 pounds.
B An infant's starting weight is 1.25 pounds.An infant's starting weight is 1.25 pounds.
C An infant's weight increases by an additional 7 pounds for each month.An infant's weight increases by an additional 7 pounds for each month.
D An infant's weight increases by an additional 1.25 pounds for each month.

Answer 1

The slope of the equation \( y = 1.25x + 7 \) represents the rate of change of the dependent variable (weight) with respect to the independent variable (age in months). In this context, the slope is 1.25, which means that for each additional month (increase in \( x \)), the weight of the infant ( \( y \)) increases by 1.25 pounds.

Therefore, the correct interpretation of the slope in this context is: D. An infant's weight increases by an additional 1.25 pounds for each month.

Answer 2

A veterinarian collected data on the association between age and mass of Boxer puppies. A line of best fit was computed. The equation for the line is: y = 17.5x + 480. Which BEST interprets the slope of the linear model?
Responses
A The predicted mass of a Boxer puppy at birth.The predicted mass of a Boxer puppy at birth.
B Every 17.5 days is associated with an additional 480 grams of mass.Every 17.5 days is associated with an additional 480 grams of mass.
C Each additional day is associated with an additional 480 grams of mass.Each additional day is associated with an additional 480 grams of mass.
D Each additional day is associated with an additional 17.5 grams of mass.

Answer 3

In the given equation \( y = 17.5x + 480 \), \( x \) represents the age of Boxer puppies, and \( y \) represents their mass.

The slope of the equation is 17.5, which indicates the change in mass (in grams) for each additional day (the unit of the independent variable, \( x \)).

Therefore, the correct interpretation of the slope in this context is: D. Each additional day is associated with an additional 17.5 grams of mass.

Answer 4

The graph shows the tip amount that 14 different customers left, based on the their bill. A trend line has been drawn for the data. The equation for the line is: y = 0.14x + 2.5. Which BEST interprets the slope of the linear model?
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Responses
A A $1 increase in the bill is associated with a $2.50 increase in tip amount.A $1 increase in the bill is associated with a $2.50 increase in tip amount.
B A $2.50 increase in the bill is associated with a $1 increase in tip amount.A $2.50 increase in the bill is associated with a $1 increase in tip amount.
C A $0.14 increase in the bill is associated with a $1 increase in tip amount.A $0.14 increase in the bill is associated with a $1 increase in tip amount.
D A $1 increase in the bill is associated with a $0.14 increase in tip amount.

Answer 5

In the equation \( y = 0.14x + 2.5 \), where \( y \) represents the tip amount and \( x \) represents the bill amount, the slope is 0.14. This slope indicates the amount by which the tip increases for each additional dollar increase in the bill.

Thus, the correct interpretation of the slope is: D. A $1 increase in the bill is associated with a $0.14 increase in tip amount.

Answer 6

A doctor collected data to determine the association between age of an infant and its weight. She modeled the equation y = 1.25x + 7 for the line of best fit. The independent variable, x, is time in months and the dependent variable, y, is weight in pounds. What does the y-intercept mean in this context?
Responses
A The infant's starting weight is 7 pounds.The infant's starting weight is 7 pounds.
B The infant's starting weight is 1.25 pounds.The infant's starting weight is 1.25 pounds.
C The infant's weight increases by an additional 7 pounds for each month.The infant's weight increases by an additional 7 pounds for each month.
D The infant's weight increases by an additional 1.25 pounds for each month.

Answer 7

In the equation \( y = 1.25x + 7 \), the y-intercept is the value of \( y \) when \( x = 0 \). In this context, \( x \) represents the age of the infant in months.

When \( x = 0 \) (which corresponds to the newborn stage of the infant), the value of \( y \) (the weight) is 7. Therefore, the y-intercept means that when the infant is just born (0 months old), its weight is 7 pounds.

Thus, the correct interpretation of the y-intercept in this context is: A. The infant's starting weight is 7 pounds.

Answer 8

A botanist collected data on the growth of sunflowers to maturity. She modeled the equation y = x + 1/2 for the line of best fit. The independent variable, x, is time in weeks and the dependent variable, y, is height in feet. What does the slope mean in this context?
Responses
A The sunflower's starting height is 1 foot.The sunflower's starting height is 1 foot.
B The sunflower's starting height is 1/2 foot.The sunflower's starting height is 1 2 foot.
C The sunflower's height increases by an additional 1 foot each week.The sunflower's height increases by an additional 1 foot each week.
D The sunflower's height increases by an additional 1/2 foot each week.

Answer 9

In the equation \( y = x + \frac{1}{2} \), the slope is the coefficient of \( x \). Here, the slope is 1, which indicates how much the height of the sunflower (in feet) increases for each additional unit of time (in weeks).

This means that for each additional week (increase in \( x \)), the height of the sunflower ( \( y \)) increases by 1 foot.

Therefore, the correct interpretation of the slope in this context is: C. The sunflower's height increases by an additional 1 foot each week.

Answer 10

Rob is saving money for a down payment on a house. He opens a savings account at his local bank and deposits $1000. He models his savings plan with the equation y = 400x + 1000 based on his current income and monthly savings rate. What is the meaning of the y-intercept in the equation?
Responses
A largest amount that he can savelargest amount that he can save
B date when he will have enough saveddate when he will have enough saved
C date his savings account was starteddate his savings account was started
D starting amount in his savings account

Answer 11

In the equation \( y = 400x + 1000 \), \( y \) represents Rob's total savings, \( x \) represents the number of months, and the constant \( 1000 \) is the y-intercept. The y-intercept represents the initial amount of money that Rob has in his savings account at the beginning (when \( x = 0 \)).

Therefore, the correct interpretation of the y-intercept in this context is: D. Starting amount in his savings account.