To determine the slope-intercept form of the linear relationship between the variables \( x \) and \( y \), we need to find the slope \( m \) and the y-intercept \( b \) of the line represented by the points given in the table.
The points are:
- \( (5, 16.5) \)
- \( (7, 21.5) \)
- \( (11, 31.5) \)
Step 1: Calculate the slope \( m \)
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \( (5, 16.5) \) and \( (7, 21.5) \):
\[ m = \frac{21.5 - 16.5}{7 - 5} = \frac{5}{2} = 2.5 \]
Step 2: Use the slope to find the y-intercept \( b \)
We can use the slope and one of the points to solve for \( b \) in the equation \( y = mx + b \).
Using the point \( (5, 16.5) \):
\[ 16.5 = 2.5(5) + b \] \[ 16.5 = 12.5 + b \] \[ b = 16.5 - 12.5 = 4 \]
So, the y-intercept is \( (0, 4) \).
Final Equation:
Thus, the equation in slope-intercept form is:
\[ y = 2.5x + 4 \]
Conclusion:
The slope is \( 2.5 \) and the y-intercept is \( (0, 4) \).
So the correct answer is: D slope 2.5, y intercept (0, 4).
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