Math Problem Statement

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.

(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.

Solution

To answer these questions, I would need to analyze the scatter plot and find the line of best fit. However, since I cannot see the scatter plot, I can guide you through the steps to approximate the equation of the line of best fit and use it to make predictions.

Part (a): Writing an approximate equation of the line of best fit

  1. Identify Two Points on the Line of Best Fit: Look for two points that the line of best fit goes through or is very close to. These points can help in finding the slope and the y-intercept.

    • Slope (m): The slope is the change in y divided by the change in x: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

    • Y-Intercept (b): The y-intercept is the value of y when x = 0. You can find this by looking at the point where the line intersects the y-axis.

  2. Equation of the Line: Once you have the slope (m) and the y-intercept (b), the equation of the line will be: y=mx+by = mx + b Round the slope and y-intercept to the nearest hundredth.

Part (b): Predicting the time spent exercising

Once you have the equation of the line from part (a), you can use it to predict the time spent exercising (y) for a student who spends 4 hours texting (x = 4).

  1. Substitute x = 4 into the equation: y=m(4)+by = m(4) + b Then calculate the value of y to predict the time spent exercising.

Let me know if you'd like further guidance, or if you have any numbers you can share from the plot for more specific help!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Linear Regression
Scatter Plots

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)
Equation of a line: y = mx + b

Theorems

Least Squares Regression

Suitable Grade Level

Grades 8-10