Which of the following represents a linear function with the same slope as the table below? *Select all that apply! (2 points) Responses Cynthia has $200 in her savings account and spends $3 per day on coffee. Cynthia has $200 in her savings account and spends $3 per day on coffee. James increases his muscle mass by 3 kg per day. James increases his muscle mass by 3 kg per day. 6x−2y=12

Question

The table it:

x = -4 f(x) = 14

x = -2 f(x) = 8

x = 3 f(x) = -7

x = 5 f(x) = -13

There is also a grapha decreasing from y intercept 10 and goes through between 2 and 4 on the x axis

Answer 1

To determine which of the provided statements represents a linear function with the same slope as the data from the table or the graph, let's analyze each part.

Analyzing the Table

The table provides the following points:

• \( (-4, 14) \)
• \( (-2, 8) \)
• \( (3, -7) \)
• \( (5, -13) \)

To find the slope, we can calculate the change in \( f(x) \) over the change in \( x \) between two points. Using the points \( (-2, 8) \) and \( (3, -7) \):

1. Calculate the change in \( y \) (f(x)): \[ \Delta y = -7 - 8 = -15 \]

2. Calculate the change in \( x \): \[ \Delta x = 3 - (-2) = 5 \]

3. Calculate the slope (m): \[ m = \frac{\Delta y}{\Delta x} = \frac{-15}{5} = -3 \]

Analyzing the Graph

You mentioned that the graph is decreasing from a y-intercept of 10 and goes through between 2 and 4 on the x-axis. The slope can be determined by the steepness and direction (since it’s decreasing, the slope should also be negative). Since it is not explicitly stated, we’d ideally want specific points for calculation. However, if we assume the decrease is consistent, we would estimate that the slope is likely negative as well.

Responses

Now we analyze each of the provided statements:

1. Cynthia's Savings:

   • Initial amount = $200
   • She spends $3 per day, therefore the slope (\(m\)) is -3.
   • This can be expressed as the linear function: \[ f(x) = 200 - 3x \]
   • This function represents a linear function with a slope of -3.

2. James's Muscle Mass:

   • James increases his muscle mass by 3 kg per day, so he has a slope of +3.
   • This can be expressed as: \[ f(x) = a + 3x \] (where \(a\) is the starting mass).
   • This slope is positive and does not match the -3 found in the table.

3. Equation:

   • The equation \(6x - 2y = 12\) can be rearranged to slope-intercept form. \[ -2y = -6x + 12 \implies y = 3x - 6 \]
   • The slope here is +3, which does not match the slope of -3 from the table.

Conclusion

Based on our analysis:

• The function representing Cynthia's savings account does have the same slope (-3).
• James's muscle increase and the equation provided do not have the same slope as the table (-3).

Thus, the correct answer is: Cynthia's savings account represents a linear function with the same slope as the table.