Question

use the drop-down menus to describe through which additional point the line of best fit passes and use that line to determine the approximate value for y when x = 9. click the arrows to choose an answer from each menu. a line of best fit passes through point a and point choose... . a point on this line would have a y-value between choose... when x = 9.

Explanation:

Step1: Identify Point A's Coordinates

Point A is at \( (2, 3) \). We need to find another point on the line of best fit. Looking at the trend, point C is at \( (6, 5) \), point D at \( (5, 4) \), but let's check the slope. Let's assume the line through A (2,3) and another point, say C (6,5). Slope \( m=\frac{5 - 3}{6 - 2}=\frac{2}{4}=0.5 \).

Step2: Find Equation of the Line

Using point - slope form \( y - y_1=m(x - x_1) \) with \( (x_1,y_1)=(2,3) \) and \( m = 0.5 \), we get \( y-3 = 0.5(x - 2) \), which simplifies to \( y=0.5x+2 \).

Step3: Predict y when x = 9

Substitute \( x = 9 \) into the equation: \( y=0.5\times9 + 2=4.5+2 = 6.5 \). Now, looking at the points, the line of best fit through A (2,3) and C (6,5) (or another appropriate point like the one with a similar trend) will have a y - value between 6 and 7 when \( x = 9 \). Also, the additional point the line of best fit passes through (along with A) is likely C (or a point with a similar trend, but from the options, if we consider the points, point C is a good candidate as it's on the trend).

Answer:

The line of best fit passes through point A and point C (or the appropriate point on the trend). A point on this line would have a \( y \) - value between 6 and 7 when \( x = 9 \). (If we follow the calculation, \( y = 6.5 \) which is between 6 and 7)