Name ______Date______Period______

Linear Equations and Slope as Rate of Change- Embedded Assessment

A 10K RUN

1. Jim was serving as a finish line judge for the the Striders 10K Run. He was interested in finding out how three of his friends were doing out on the course. He was able to learn the following information from racing officials at different locations along the course.

-Matuba is running at a strong, steady rate of 320 meters every minute after running the first 1400 meters in a time of 5 minutes.

Use the information given above regarding Matuba’s progress toward the finish line and create a linear equation model.Matuba’s model can be written in the POINT-SLOPE FORM. Consider the information given- Matuba ran the first 1400 meters in 5 minutes.Use x as the number of minutes since the race began and y as the number of meters completed.

What does the wording “strong, steady rate of 320 Meters per minute” mean to you in this example?

Now, use your two variables and create an ordered pair (x,y) also known as a “point”. Take the number given for slope “m” and the “point” and write the equation in Point-Slope Form and then write in Slope-Intercept Form, and finally Standard Form.

Slope=

Point-Slope Form:

Slope-Intercept Form:

Standard Form:

-Rodriguez ran the first 2000 meters in 6 minutes, before he settled into his steady pace passing the 4400 meter mark at 14 minutes.

This information above gives two points in time which you can use to write the equation of a line passing through the given pair of points. Remember that in order to write an equation in Point-Slope Form, you must have a “point” and a “slope”.

So, find the slope first, pick one of the points, and write the equation. Remember x is minutes and y is meters.

Slope=

Point-Slope Form:

Slope-Intercept Form:

Standard Form:

-According to his calculations, Donavan feels he can equal his best running time of 32 minutes for 10,000 meters over this course.

This information about Donavan only gives the finish line point- (32, 10,000). What would the point be for the starting point of the race? Once you have decided on this point, you can get started on writing the equation of the line in Point-Slope Form. Once you have the equation in Point-Slope Form, please also write in Slope-Intercept Form and then finally in Standard Form.

Slope=

Point-Slope Form:

Slope-Intercept Form:

Standard Form:

  1. Find the order in which the three runners will finish the 10,000 meter (10K) race. You will need to find the finish time for each runner separately using your equations from above and rank 1st, 2nd, and 3rd place. Hint- you have been given the distance “y”, so you will be solving for “x” time.
  1. What order would the runners have been in at the 5000 meter mark?
  1. What is the domain of the linear model for Donavan?
  1. What is the y-intercept of the equation your wrote for Matuba? Hint- take your Point-Slope Formula and write it in Slope-Intercept form. Does this number have any significance to this model?
  1. What is the slope of the linear model for Rodriguez and what does it mean in terms of running this race?