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Valerie Perez
8th Grade
ASSESSMENT - Math 8 Sem A Unit 5 Retest
Question Id : 521463
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Question
Lilly wants to determine the association between her deposits and her savings account balance. She modeled the equation y = 75x + 100 for the line of best fit. The independent variable, x, is deposits and the dependent variable, y, is account balance. What does the y-intercept mean in this context?
Responses
A The starting savings account balance is $75.The starting savings account balance is $75.
B The starting savings account balance is $100.The starting savings account balance is $100.
C The account balance increases by an additional $75 for each deposit.
The account balance increases by an additional $75 for each deposit.
D The account balance increases by an additional $100 for each deposit.
The account balance increases by an additional $100 for each deposit.
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11 answers
The equation provided is \( y = 75x + 100 \), where \( y \) represents the savings account balance and \( x \) represents the deposits. In this equation, the y-intercept (the constant term) is \( 100 \).
In this context, the y-intercept represents the initial savings account balance when no deposits have been made (when \( x = 0 \)). Therefore, the appropriate interpretation of the y-intercept is:
B. The starting savings account balance is $100.
In the equation \( y = x + \frac{1}{2} \), where \( y \) represents the height of the sunflower in feet and \( x \) represents time in weeks, the y-intercept is \(\frac{1}{2}\).
In this context, the y-intercept represents the height of the sunflower when no time has passed (when \( x = 0 \)). Therefore, the appropriate interpretation of the y-intercept is:
B. The sunflower's starting height is \(\frac{1}{2}\) foot.
Let's break down the equation \( y = 2,500x + 32,500 \) to fill in the responses correctly.
Now, for the changes in the equation:
If the starting salary for a new employee is changed to $35,000 and the yearly salary increase is unchanged, the new equation would be: \[ y = 2,500x + 35,000 \]
If the yearly salary increase is changed to $3,000 and the starting salary remains the same, the new equation would be: \[ y = 3,000x + 32,500 \]
Based on this breakdown, the filled responses are:
In the equation \( y = 295 - 5x \), where \( y \) represents the weight in pounds and \( x \) represents time in weeks, the y-intercept is \( 295 \).
In this context, the y-intercept indicates the man's weight at the start of his diet (when \( x = 0 \)). Therefore, the appropriate interpretation of the y-intercept is:
C. The man weighed 295 pounds at the start of his diet.
To find the equation that relates the time spent watching TV (independent variable, \( x \)) to the time spent doing homework (dependent variable, \( y \)), we can first analyze the given data and then calculate the slope and y-intercept.
Here’s a summary of the information from the table:
\[ \begin{array}{|c|c|} \hline \text{Time spent watching TV (hours)} (x) & \text{Time spent doing homework (hours)} (y) \ \hline 2 & 14 \ 5 & 10 \ 7 & 9 \ 8 & 6 \ 11 & 5 \ 12 & 3 \ \hline \end{array} \]
The slope \( m \) is calculated using the formula:
\[ m = \frac{(y_2 - y_1)}{(x_2 - x_1)} \]
We can select two points from the data. Let's take the points (2, 14) and (12, 3).
\[ m = \frac{3 - 14}{12 - 2} = \frac{-11}{10} = -1.1 \]
We can use the slope-intercept form of the line:
\[ y = mx + b \]
We can use one of the points to solve for \( b \). Let’s use the point (2, 14):
\[ 14 = -1.1(2) + b \]
Calculating:
\[ 14 = -2.2 + b \ b = 14 + 2.2 = 16.2 \]
Now that we have both \( m \) and \( b \), we can write the final equation:
\[ y = -1.1x + 16.2 \]
The equation that describes the relationship between the time spent watching TV and the time spent doing homework is:
\[ y = -1.1x + 16.2 \]
This indicates that for each hour spent watching TV, the time spent doing homework decreases by approximately 1.1 hours, starting from a theoretical maximum of 16.2 hours of homework when no TV is watched.
While I can't directly create graphical content like a scatter plot, I can guide you on how to create one using the data provided. You can use tools like Microsoft Excel, Google Sheets, or even graphing software. Here's a step-by-step guide using both Excel and Google Sheets:
A1: Time spent watching TV (hours)
A2: 2
A3: 5
A4: 7
A5: 8
A6: 11
A7: 12
B1: Time spent doing homework (hours)
B2: 14
B3: 10
B4: 9
B5: 6
B6: 5
B7: 3
After inputting, your plotted points would look like this:
The scatter plot will illustrate how the time spent watching TV (x-axis) is related to the time spent doing homework (y-axis). Generally, you should see a downward trend, indicating that as time watching TV increases, the time spent on homework decreases, which aligns with the equation you derived earlier.
Once you follow these steps, you will have a scatter plot representing the data visually. If you have access to any specific plotting tools, let me know, and I can tailor the instructions accordingly!
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