Questions: Given the line of best fit for a set of data points with the equation y=5x-2.5, what is the residual for the point (5,26)? A. -3.5 B. 26 C. -26 D. 3.5

Solution Steps

Given the line of best fit represented by the equation

\[ y = 5x - 2.5 \]

we need to find the predicted \( y \) value for the point \( (5, 26) \). Substituting \( x = 5 \) into the equation:

\[ y_{\text{predicted}} = 5(5) - 2.5 = 25 - 2.5 = 22.5 \]

The residual is defined as the difference between the actual \( y \) value and the predicted \( y \) value. For the point \( (5, 26) \), the actual \( y \) value is \( 26 \). Thus, the residual can be calculated as follows:

\[ \text{Residual} = y_{\text{actual}} - y_{\text{predicted}} = 26 - 22.5 = 3.5 \]

From the calculated residual of \( 3.5 \), we compare it with the provided options:

• A. -3.5
• B. 26
• C. -26
• D. 3.5

The residual matches option D.

Final Answer