Unicycle Adventures: Analyzing Residuals

1. Check it out! 4.2.3: Analyzing Residuals

2. Felicia is learning to ride a unicycle. She started at her house, which is at the origin. She went 2 blocks east and wasn’t able to successfully ride the unicycle. Then she started going north toward her friend’s house. After many failed attempts and falling off for 4 blocks, she had success for 2 blocks. Plot the points (2, 4) and (2, 6) on a coordinate plane. Find the distance between the two points. How far did Felicia successfully ride her unicycle? 4.2.3: Analyzing Residuals

3. Felicia is going to sell unicycle pins to raise money for medical research. She spent $2 of her own money to buy the pins and will sell each pin for $4. Her revenue can be modeled by the function y= 4x – 2. Plot the function y = 4x – 2 over the domain of all real numbers. 4.2.3: Analyzing Residuals

4. Plot the points (2, 4) and (2, 6) on a coordinate plane. The first number in each ordered pair is the x-value, and the second number is the y-value. 4.2.3: Analyzing Residuals

5. Find the distance between the two points. How far did Felicia successfully ride her unicycle? Look at the location of the points on the coordinate plane. The two points have the same x-value, so the only distance between the two points is a vertical distance. The distance is the absolute value of the difference between the two y-values: |6 – 4| = 2. Felicia rode 2 blocks. 4.2.3: Analyzing Residuals

6. Plot the function y = 4x – 2 over the domain of all real numbers. An equation of the form y = mx + b is a linear function. The graph is a line, so only two points are needed to create the graph. Evaluate the function at two values of x to find two points on the line. For example, evaluate the function at x = 0 and x = 1. y = 4(0) – 2 = –2 Substitute 0 for x. y = 4(1) – 2 = 2 Substitute 1 for x. 4.2.3: Analyzing Residuals

7. Two points on the line are (0, –2) and (1, 2). Plot these points, and then draw a line through them. 4.2.3: Analyzing Residuals