Question

the scatter plot shows the time spent watching tv, x, and the time spent doing homework, y, by each of 24 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 = -0.5x + 20 )

Explanation:

Step1: Identify the trend

The scatter plot shows a negative correlation between time spent watching TV (x) and time spent doing homework (y). As x increases, y decreases.

Step2: Estimate the slope

To find the slope (m) of the line of best fit, we can use two points on the line. Looking at the scatter plot, when x = 0, y is around 20 (y-intercept, b). When x = 28, y is around 6 (estimating from the plot). So the slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{6 - 20}{28 - 0}=\frac{- 14}{28}=- 0.5\)

Step3: Write the equation

The equation of a line is \( y = mx + b\). We found \( m=-0.5\) and \( b = 20\) (from the y - intercept when x = 0). So the equation is \( y=-0.5x + 20\) (rounding to the nearest hundredth, the coefficients are already to the hundredth place as - 0.50x+20.00, but - 0.5x + 20 is also correct as - 0.5 is equivalent to - 0.50)

Answer:

\(y=-0.5x + 20\)