Question

the 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 below. (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 4 hours texting. round your prediction to the nearest hundredth. \square hours

Explanation:

Step1: Identify two points on the line

Looking at the scatter plot, we can approximate two points on the line of best fit. Let's take (1, 9) and (9, 1) as approximate points.

Step2: Calculate the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points (1, 9) and (9, 1):
$m = \frac{1 - 9}{9 - 1} = \frac{-8}{8} = -1.00$ (rounded to nearest hundredth)

Step3: Find the y-intercept (b)

Using the point-slope form $y - y_1 = m(x - x_1)$ with point (1, 9) and $m = -1$:
$y - 9 = -1(x - 1)$
$y - 9 = -x + 1$
$y = -x + 10.00$ (So the equation is $y = -1.00x + 10.00$)

Step4: Predict for x = 4 (part b)

Substitute x = 4 into the equation $y = -x + 10$:
$y = -4 + 10 = 6.00$

Answer:

(a) $y = -1.00x + 10.00$
(b) 6.00