Question

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nina graphs the data in the table and writes the rounded values for a and b as shown below for the regression line y = ax + b.
a ≈ 0.36
b ≈ -10.5
which explains how the fertilizer affects the growth of the plant?

• the trend line is y = 0.36x - 10.5, which means that the rate of change in height is 0.36 inches per ounce of fertilizer.
• the trend line is y = 0.36x - 10.5, which means that the rate of change in height is 10.5 inches per ounce of fertilizer.
• the trend line is y = -10.5x + 0.36, which means that the rate of change in height is 0.36 inches per ounce of fertilizer.
• the trend line is y = -10.5x + 0.36, which means that the rate of change in height is 10.5 inches per ounce of fertilizer.

Explanation:

Step1: Recall the slope-intercept form

The regression line is given by \( y = ax + b \), where \( a \) is the slope (rate of change) and \( b \) is the y-intercept.

Step2: Identify the slope and intercept

From the problem, \( a = 0.36 \) (slope) and \( b = -10.5 \) (y-intercept). So the equation is \( y = 0.36x - 10.5 \).

Step3: Interpret the slope

The slope (rate of change) of \( 0.36 \) means for each ounce of fertilizer (x), the height (y) increases by 0.36 inches. Now check the options:

• Option 1: Matches the equation \( y = 0.36x - 10.5 \) and the correct interpretation of the slope (rate of change in height is 0.36 inches per ounce of fertilizer).
• Option 2: Incorrectly interprets the slope as 10.5 (10.5 is the y-intercept, not the slope).
• Option 3: Incorrect equation (should be \( y = 0.36x - 10.5 \), not \( y = -10.5x + 0.36 \)).
• Option 4: Incorrect equation and incorrect slope interpretation.

Answer:

The trend line is \( y = 0.36x - 10.5 \), which means that the rate of change in height is 0.36 inches per ounce of fertilizer.