Question

a line of best fit was drawn to the plotted points in a data set below. based on the line of best fit, for what y-value does x = 16?

Explanation:

Step1: Identify the line of best fit

The line of best fit is the straight line drawn through the data points. We can see points on this line, for example, when \( x = 4 \), \( y = 14 \); when \( x = 8 \), \( y = 12 \); when \( x = 12 \), \( y = 10 \); when \( x = 16 \), we need to find \( y \).

Step2: Determine the pattern or slope

Looking at the points: from \( x = 4 \) ( \( y = 14 \)) to \( x = 8 \) ( \( y = 12 \) ), the change in \( x \) is \( 8 - 4 = 4 \), and the change in \( y \) is \( 12 - 14 = -2 \). So the slope \( m=\frac{\Delta y}{\Delta x}=\frac{-2}{4}=-\frac{1}{2} \).

Step3: Use the slope to find \( y \) at \( x = 16 \)

We can use the point - slope form or just observe the pattern. From \( x = 4 \) to \( x = 16 \), the change in \( x \) is \( 16 - 4 = 12 \). Since the slope is \( -\frac{1}{2} \), the change in \( y \) is \( m\times\Delta x=-\frac{1}{2}\times12=- 6 \).

Starting from \( y = 14 \) (when \( x = 4 \)), when \( x = 16 \), \( y=14-6 = 8 \).

Or we can observe the pattern of the line: when \( x = 4 \), \( y = 14 \); \( x = 8 \), \( y = 12 \); \( x = 12 \), \( y = 10 \). We can see that for every increase of 4 in \( x \), \( y \) decreases by 2. From \( x = 12 \) to \( x = 16 \) (an increase of 4 in \( x \)), \( y \) will decrease by 2 from \( y = 10 \) (when \( x = 12 \)) to \( y=10 - 2=8 \).

Answer:

\( 8 \)