Question

the scatter plot shows the time spent watching tv, x, and the time spent doing homework, y, by each of 23 students last week. use the scatter plot to answer the parts below. (note that you can use the graphing tools to help you approximate the line.)
scratch area (not part of answer)
(a) write an approximate equation of the line of best fit. round the coefficients to the nearest hundredth.
y =
(b) using your equation from part (a), predict the time spent doing homework for a student who spends 12 hours watching tv. round your prediction to the nearest hundredth.
hours

Explanation:

Step1: Find two points on the line

Looking at the scatter plot, we can estimate two points. Let's take (4, 24) and (28, 4) as approximate points on the line of best fit.

Step2: Calculate the slope (m)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Substituting the points: \( m = \frac{4 - 24}{28 - 4} = \frac{-20}{24} \approx -0.83 \)

Step3: Find the y-intercept (b)

Using the point-slope form \( y - y_1 = m(x - x_1) \) with (4, 24): \( y - 24 = -0.83(x - 4) \). Simplifying: \( y = -0.83x + 3.32 + 24 \), so \( y \approx -0.83x + 27.32 \) (this is the equation for part a).

Step4: Predict for x = 12 (part b)

Substitute \( x = 12 \) into the equation: \( y = -0.83(12) + 27.32 = -9.96 + 27.32 = 17.36 \)

Answer:

(a) \( y = -0.83x + 27.32 \) (values may vary slightly based on point selection)
(b) 17.36 hours