Question

(a) what is the linear model for the data?
f(x) = 1229x + 24552
(type your answer in slope-intercept form. use integers or decimals for any numbers in the expression. round to the nearest hundredth as needed )
graph f and a scatter diagram of the data on the same coordinate axes. choose the correct graph below.
○ a. graph with y-axis 30000, 28000, 26000, 24000; x-axis -2, 0, 2, 4; positive - slope line and scatter points
○ b. graph with y-axis 30000, 28000, 26000, 24000; x-axis -2, 0, 2, 4; negative - slope line
○ c. graph with y-axis 30000, 28000, 26000, 24000; x-axis -2, 0, 2, 4; positive - slope line
○ d. graph with y-axis 30000, 28000, 26000, 24000; x-axis -2, 0, 2, 4; negative - slope line

Explanation:

To determine the correct graph, we analyze the linear model \( f(x) = 1229x + 24552 \):

Step 1: Analyze the Slope

The slope (\( m = 1229 \)) is positive, so the line should be increasing (rising from left to right). This eliminates options B and D (which have negative slopes, decreasing lines).

Step 2: Analyze the y - Intercept

The y - intercept (\( b = 24552 \)) is the value of \( f(x) \) when \( x = 0 \). Let’s check the y - intercepts of the remaining options (A and C):

• For option A: When \( x = 0 \), the line appears to pass near \( y \approx 24000 \), but our model has \( f(0)=24552 \).
• For option C: When \( x = 0 \), the line passes near \( y = 24552 \) (consistent with the y - intercept of the model).

Step 3: Verify the Trend

Since the slope is positive, the line should rise as \( x \) increases. Option C shows an increasing line that matches the positive slope and the correct y - intercept.

Answer:

C