Question

which equation represents a line of best fit for the scatter plot?

a ( y=\frac{1}{15}x )
b ( y = 15x )
c ( y=\frac{1}{15}x+2\frac{1}{2} )
d ( y = 15x+2\frac{1}{2} )

Explanation:

Step1: Identify trend direction

The scatter plot shows a positive linear trend (y increases with x).

Step2: Estimate slope

Pick two points: (0, ~3) and (1, ~16). Slope = (16-3)/(1-0) = 13, close to 15.

Step3: Estimate y-intercept

When x=0, y≈3, close to \(2\frac{1}{2}\).

Step4: Match with options

Option D has slope 15 and intercept \(2\frac{1}{2}\), fitting the trend.

Answer:

D. \(y=15x + 2\frac{1}{2}\)