Question

scatter plot shows the time spent texting, x, and the time spent exercising, y, by each of 23 students last week. use the scatter plot to answer the parts w. (note that you can use the graphing tools to help you approximate the line.) (a) write an approximate equation of the line of best fit. round the coefficients to the nearest hundredth. y = \square (b) using your equation from part (a), predict the time spent exercising for a student who spends 6 hours texting. round your prediction to the nearest hundredth. \square hours

Explanation:

Step1: Identify line of best fit points

Choose two points on the approximate line of best fit, e.g., $(0, 8.5)$ and $(10, 0.5)$.

Step2: Calculate slope

Slope $m = \frac{y_2-y_1}{x_2-x_1} = \frac{0.5-8.5}{10-0} = \frac{-8}{10} = -0.80$

Step3: Find y-intercept

The y-intercept $b$ is the y-value when $x=0$, so $b=8.50$. The line equation is $y = -0.80x + 8.50$.

Step4: Substitute $x=6$ into equation

Substitute $x=6$ into $y = -0.80x + 8.50$:
$y = -0.80(6) + 8.50 = -4.80 + 8.50$

Step5: Compute predicted value

Calculate the final value: $y = 3.70$

Answer:

(a) $y = -0.80x + 8.50$
(b) $3.70$ hours