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our teacher surveyed the class to determine the number of hours that each student spent on social media. Your teacher created a table and scatterplot graph that displayed the number of hours and the average final grade based on the hours. The trend line (equation) for the data is y=−7.2x+98.9

. Interpret the slope. How many points does the average final grade decrease for 1 hour on social media?(1 point)

11 answers

The equation of the trend line is given as \( y = -7.2x + 98.9 \), where:

  • \( y \) represents the average final grade,
  • \( x \) represents the number of hours spent on social media,
  • \( -7.2 \) is the slope of the line,
  • \( 98.9 \) is the y-intercept.

The slope of the line, which is \( -7.2 \), indicates that for each additional hour spent on social media, the average final grade decreases by 7.2 points.

In summary, the average final grade decreases by 7.2 points for each additional hour spent on social media.

Your teacher surveyed the class to determine the number of hours that each student spent on social media. Your teacher created a table and scatterplot graph that displayed the number of hours and the average final grade based on the hours. The trend line (equation) for the data is y=−7.2x+98.9
. Interpret the y
-intercept. What is the average grade if a student was on social media for 0 hours?(1 point)

The y-intercept of the equation \( y = -7.2x + 98.9 \) is the value of \( y \) when \( x \) is 0. In this context, the y-intercept \( 98.9 \) represents the average final grade for a student who does not spend any time on social media (0 hours).

Therefore, if a student was on social media for 0 hours, their average final grade would be 98.9.

Your company asked you to analyze the investment of their advertising campaign. You create a scatterplot graph of the advertising dollars spent on advertising, x
, and compare it to the revenue generated, y
, for January to December of the campaign. You find the equation of the trend line to be y=2.53x+43
. Predict the revenue generated if your company invests $200.00 in advertising. Write the revenue in dollars and cents.(1 point)
The revenue generated for a $200.00 investment in advertising is $
.

To predict the revenue generated if the company invests $200.00 in advertising, you can substitute \( x = 200 \) into the equation of the trend line, which is given by:

\[ y = 2.53x + 43 \]

Substituting 200 for \( x \):

\[ y = 2.53(200) + 43 \]

Calculating:

\[ y = 506 + 43 \] \[ y = 549 \]

Therefore, the revenue generated for a $200.00 investment in advertising is $549.00.

You work for a manufacturing company on a production line that manufactures cell phones. You are paid $30 a day plus $0.75 for each phone that you assemble. Predict your wages if you assemble 100 phone in one day, using the equation of the trend line y=0.75x+30
, where x
is the number of phones assembled in one day and y
is the total wages. Write your wages in dollars and cents.(1 point)
Your wages are $
.

To predict your wages if you assemble 100 phones in one day, you can substitute \( x = 100 \) into the equation of the trend line:

\[ y = 0.75x + 30 \]

Substituting 100 for \( x \):

\[ y = 0.75(100) + 30 \]

Calculating:

\[ y = 75 + 30 \] \[ y = 105 \]

Therefore, your wages for assembling 100 phones in one day are $105.00.

You work for a manufacturing company on a production line that manufactures cell phones. You are paid $20 a day plus $1.50 for each phone that you assemble. Interpret the slope and y-intercept of the equation of the trend line y=1.50x+20.(1 point)
Responses

The slope means that, for every phone assembled, you receive $20. The y-intercept means that you receive $1.50 a day regardless of the number of phones produced.
The slope means that, for every phone assembled, you receive $20. The y -intercept means that you receive $1.50 a day regardless of the number of phones produced.

The slope means that, for every 20 phones assembled, you receive $1.50. The y-intercept means that you receive $20 a day regardless of the number of phones produced.
The slope means that, for every 20 phones assembled, you receive $1.50. The y -intercept means that you receive $20 a day regardless of the number of phones produced.

The slope means that, for every phone assembled, you receive $1.50. The y-intercept means that you receive $20 a day regardless of the number of phones produced.
The slope means that, for every phone assembled, you receive $1.50. The y -intercept means that you receive $20 a day regardless of the number of phones produced.

The slope means that, for every 1.50 phones assembled, you receive $1. The y-intercept means that you receive $20 a day regardless of the number of phones produced.

To interpret the slope and y-intercept of the equation \( y = 1.50x + 20 \):

  • Slope (1.50): This means that for every phone assembled, you receive an additional $1.50. This reflects the variable pay based on the number of phones you produce.

  • Y-intercept (20): This means that you receive $20 a day regardless of the number of phones produced. This reflects your fixed daily wage.

Based on this interpretation, the correct response is:

The slope means that, for every phone assembled, you receive $1.50. The y-intercept means that you receive $20 a day regardless of the number of phones produced.

The population growth of a state since 2000 in millions of people is represented by a linear model. Using the trend line, y=0.83x+30, predict the population, y, in the year 2030. Let x=30 because the year 2030 is 30 years after the year 2000.(1 point)
Responses

In 2030, the population of the state will be 0.83 million people.
In 2030, the population of the state will be 0.83 million people.

In 2030, the population of the state will be 30.03 million people.
In 2030, the population of the state will be 30.03 million people.

In 2030, the population of the state will be 60.83 million people.
In 2030, the population of the state will be 60.83 million people.

In 2030, the population of the state will be 54.9 million people.

To predict the population in the year 2030 using the trend line \( y = 0.83x + 30 \), we need to substitute \( x = 30 \) (since 2030 is 30 years after 2000) into the equation.

\[ y = 0.83(30) + 30 \]

Calculating:

\[ y = 24.9 + 30 \] \[ y = 54.9 \]

Therefore, the predicted population of the state in 2030 is 54.9 million people.

So, the correct response is:

In 2030, the population of the state will be 54.9 million people.