Questions: 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= (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. hours

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=

(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.
hours

Transcript text: 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.) 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 exercising for a student who spends 4 hours texting. Round your prediction to the nearest hundredth. hours

Solution

Solution Steps

Step 1: Approximate the line of best fit

Draw a line through the scatter plot that best represents the relationship between the time spent texting and the time spent exercising. The line should have roughly equal numbers of points above and below it. The line appears to go through approximately (2, 8) and (7, 3).

Step 2: Calculate the slope

The slope is the change in y divided by the change in x. Using the points (2, 8) and (7, 3), the slope is (3 - 8) / (7 - 2) = -5 / 5 = -1.

Step 3: Calculate the y-intercept

Use the point-slope form of a linear equation: y - y1 = m(x - x1). Using the point (2, 8) and slope -1, we have y - 8 = -1(x - 2). Simplifying, we get y - 8 = -x + 2, and then y = -x + 10.

Step 4: Predict the time spent exercising

If a student spends 4 hours texting, substitute x = 4 into the equation: y = -4 + 10 = 6.