Which statement correctly interprets the slope?

Question

(1 point)
Responses

The time on the tightrope goes up about 9 minutes for every 5 people.

The time on the tightrope goes up by about 2 people per minute.
The time on the tightrope goes up by about 2 people per minute.

The time on the tightrope goes up about 5 minutes for every 9 people.
The time on the tightrope goes up about 5 minutes for every 9 people.

The time on the tightrope goes up about 1 minute for every 1 person.
The time on the tightrope goes up about 1 minute for every 1 person.
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Answer 1

To correctly interpret the slope of a graph, you need to understand what the slope represents in the context of the variables involved. The slope indicates how much one variable changes in relation to the change in another variable.

Without the specific equation or context from which the slope is derived, I can help explain how to interpret a slope.

• If the slope is given as "5 minutes per 9 people," this means for every increase of 9 people, the time on the tightrope increases by 5 minutes.
• If the slope is "2 people per minute," it indicates that for every minute, the number of people increases by 2.
• A slope of "1 minute per 1 person" means that for each additional person, it takes an additional minute on the tightrope.

Reviewing the options provided, the correct interpretation would depend on the actual slope value.

If you have specific slope values, you can select the corresponding interpretation based on those values. If none of the statements align with your slope value, then none of them accurately interpret the slope.

Answer 2

Use the graph to fill in the blanks.

(4 points)
A. The y-intercept is (Response area)

B. In context, the y-intercept means (Response area)

C. The x-intercept is (Response area)

D. In context, the x-intercept means (Response area)

responses
when the batter has been used for 9 hours, the battery life is 0%
(4, 50)
when the battery has been used for 0 hours, the battery life is 0%
when the battery has been used for 0 hours, the battery life is 9%
(0, 100)
when the battery has been used for 9 hours, the battery life is 100%
(0, 0)
(0, 9)
(9, 0)
when the battery has been used for 0 hours, the battery life is 100%

Answer 3

To fill in the blanks based on typical interpretations of the y-intercept and x-intercept in the context of a graph showing battery life as a function of usage hours, here's the likely completion:

A. The y-intercept is (0, 100).
B. In context, the y-intercept means when the battery has been used for 0 hours, the battery life is 100%.
C. The x-intercept is (9, 0).
D. In context, the x-intercept means when the battery has been used for 9 hours, the battery life is 0%.

This interpretation indicates that the battery starts fully charged (100%) when no hours have been used, and it runs out of battery (0%) after 9 hours of use.

Answer 4

Which equation BEST represents the line of best fit for the scatter plot?

(1 point)
Responses

y=−3x+2
y is equal to negative 3 x plus 2

y=x−3
y is equal to x minus 3

y=x+3
y is equal to x plus 3

y=−3x−2

Answer 5

To determine which equation best represents the line of best fit for a scatter plot, you would typically need to analyze the plot visually or have data points to compare the potential trends.

Without the specific scatter plot in question, here are some general tips on how to decide:

• y = -3x + 2: This line has a negative slope and a positive y-intercept, meaning it decreases as x increases.
• y = x - 3: This line has a positive slope of 1, indicating a direct relationship where both x and y increase together, starting from -3 on the y-axis.
• y = x + 3: Similar to the previous equation, this line also has a positive slope and passes through positive y at y = 3.
• y = -3x - 2: Like the first option, this equation has a negative slope, decreasing more steeply, and a negative y-intercept.

If the scatter plot shows a negative correlation with a relatively steep decline, the best options would be y = -3x + 2 or y = -3x - 2. If it demonstrates a positive correlation, you might choose y = x - 3 or y = x + 3.

To choose the best option, consider the slope and intercept values from the scatter plot and select the equation that closely resembles the trend of the data points. If you can share more details about the scatter plot or the context, I can provide a more precise answer.

Answer 6

This data was taken from an unbiased study of ice cream sales.

(2 points)
A. What is the equation of the line of best fit for this data? (Response area)

B. What conclusion is appropriate? (Response area )

responses
y = 30x - 150
y = 10x
y = -100x + 30
the temperature rising causes ice cream sales to go up
as the temperature rises, ice cream sales go down
as the temperature goes down, ice cream sales go up
as the temperature goes up, ice cream sales go up

Answer 7

To appropriately select the answers for this data regarding ice cream sales in relation to temperature, let’s analyze the questions:

A. What is the equation of the line of best fit for this data?

Given the context of ice cream sales, an equation that suggests a positive relationship between temperature and sales is most logical. Therefore, one of the following options should represent this:

• y = 30x - 150: This implies a positive correlation.
• y = 10x: This also indicates a positive correlation.
• y = -100x + 30: This indicates a negative correlation.

Since ice cream sales are typically expected to increase with rising temperatures, choose either of the first two equations. The specific choice may depend on additional context.

Select:

• y = 30x - 150 or y = 10x (if one is not prioritized over the other, depending on additional context, pick accordingly).

B. What conclusion is appropriate?

Considering the relationship between temperature and ice cream sales, the logical conclusion is:

• as the temperature goes up, ice cream sales go up: This conclusion reflects the typical understanding that warmer weather encourages ice cream sales.

Select:

• as the temperature goes up, ice cream sales go up.

Summary Response:

• A: y = 30x - 150 (or y = 10x)
• B: as the temperature goes up, ice cream sales go up.

Answer 8

Desmos Graphing Calculator: Use the link to access the Graphing Calculator. Open a table and input the data. Ask the calculator for a Linear Regression Line (Line of Best Fit)

(3 points)
A. What is the equation for the Linear Regression Line? (Response area)

B. There is a (Response area) correlation between the test marks and the homework marks.

C. The slope of the line of best fit can be used to make a probabilistic interpretation that states (response area)

responses the test mark decreases 0.7 pts for every 1 pt on the homework mark.
y = 0.7x - 38
the homework mark increases 37 pts for every 1 pt on the test.
negative
y = 0.89x - 36.7
the homework mark increases 0.89 points for every 1 pt on the test mark.
positive
y = -x + 37
y = -37x + 1
the test mark increases 1 pt for every 1 pt on the homework mark.
no correlation

Answer 9

To correctly fill out the responses for the Linear Regression Line based on homework marks and test marks, we can generally consider the relationships and interpretations expected in this context. Here’s how to respond to each section without the specific data, assuming a positive correlation is typical in educational contexts:

A. What is the equation for the Linear Regression Line?

This equation describes the best fit line derived from the data. Based on your options, it could be:

Select:

• y = 0.7x - 38 (if the regression gives a positive slope and y-intercept).
• y = 0.89x - 36.7 (if the regression gives an even closer fit).

B. There is a (Response area) correlation between the test marks and the homework marks.

If the regression line has a positive slope, which would typically imply that higher homework marks correspond to higher test marks, then you would select:

Select:

• positive correlation.

C. The slope of the line of best fit can be used to make a probabilistic interpretation that states (response area).

The slope indicates how much the test mark increases for every point increase in the homework mark. Depending on the slope you obtained, you would make a different choice. Assuming you choose one of the slopes, it could be:

• If y = 0.7x - 38: Select: the test mark increases 0.7 pts for every 1 pt on the homework mark.
• If y = 0.89x - 36.7: Select: the test mark increases 0.89 pts for every 1 pt on the homework mark.

Summary Responses:

• A: y = 0.7x - 38 (or y = 0.89x - 36.7)
• B: positive
• C: the test mark increases 0.7 pts for every 1 pt on the homework mark (or the test mark increases 0.89 pts for every 1 pt on the homework mark).

Please replace the selected options with those that correspond to the actual data you analyze using the Desmos Graphing Calculator.

Answer 10

The scatter plot shows the relationship between combined SAT score and first semester college GPA.

Choose all statements that are correct.

(3 points)
Responses

The line of best fit shows that the combined SAT Score and first semester SAT have a negative correlation.
The line of best fit shows that the combined SAT Score and first semester SAT have a negative correlation.

A reasonable prediction SAT score of 1700 is a GPA of 3.0.
A reasonable prediction SAT score of 1700 is a GPA of 3.0.

The line of best fit can be used to make predictions of GPA based on SAT score.
The line of best fit can be used to make predictions of GPA based on SAT score.

This is not an accurate line of best fit because it doesn't hit the lowest point.
This is not an accurate line of best fit because it doesn't hit the lowest point.

The line of best fit gives the best approximation of the association between SAT score and GPA.
The line of best fit gives the best approximation of the association between SAT score and GPA.

A reasonable prediction SAT score of 2100 is a GPA of 3.5.
A reasonable prediction SAT score of 2100 is a GPA of 3.5.

Answer 11

To determine which statements are correct regarding the scatter plot showing the relationship between combined SAT scores and first semester college GPA, we need to consider typical characteristics of such data.

• The line of best fit shows that the combined SAT Score and first semester SAT have a negative correlation.
  This statement is likely incorrect. Typically, higher SAT scores correlate positively with higher GPAs, indicating a positive correlation.

• A reasonable prediction SAT score of 1700 is a GPA of 3.0.
  This statement could be correct depending on the actual line of best fit shown in the scatter plot. You would need to refer to your graph for validation.

• The line of best fit can be used to make predictions of GPA based on SAT score.
  This statement is correct. The purpose of a line of best fit is indeed to be used for predictions based on the correlation observed in the data.

• This is not an accurate line of best fit because it doesn't hit the lowest point.
  This statement is likely incorrect. A line of best fit does not need to pass through all points or hit the lowest point. It represents the trend in the data, not all data points.

• The line of best fit gives the best approximation of the association between SAT score and GPA.
  This statement is correct. The line of best fit is intended to provide the best estimate of the relationship between the two variables.

• A reasonable prediction SAT score of 2100 is a GPA of 3.5.
  This statement could also be correct depending on where the SAT score of 2100 falls relative to the line of best fit in your scatter plot.

Summary of Correct Statements:

1. The line of best fit can be used to make predictions of GPA based on SAT score.
2. The line of best fit gives the best approximation of the association between SAT score and GPA.

If you find confirmation of specific GPA predictions associated with SAT scores from your scatter plot, you can also affirm or reject those corresponding statements.