Jack was serving as a finish line judge for a 10K run. He was interested in finding out how 3 of his friends did during the race. He was able to find out the following information from the racing officials:
Matuba is running at a steady rate of 320 meters every minute, after running the first 1400 meters in a time of 5 minutes.
Rod ran the first 2000 meters in 6 minutes, before settling into his pace passing the 4400 meter mark at 14 minutes.
Donovan had the following times and meters recorded:
- Write an equation in point-slope form and then simplify to slope-intercept for each runner.
Matuba:Rod:Donovan:
- In what order will the runners finish the 10K run? Explain using mathematical reasoning. (Hint: 1 K = 1000 m)
- In what order will the runners have passed the halfway mark in the race (5K)? Justify your answer with mathematical reasoning.
- Identify the slope for Rod. Interpret the meaning of the slope in the context of the problem.
- Identify the domain for Matuba.
6.Write the equation for Donovan in standard form.
Directions: Using the information given, write an equation in slope-intercept form.
- m = 15, (3, -1) 8. (-1, -1) and (3, 1)9. -4x + 3y = -21
10. (5, -7) and (5, -9)11. 12.
Directions: Answer each question, make sure to show all work.
13. Several linear equations are shown. Arrange the equations in order from steepest slope to least steep slope.
- y – 2 = 6(x – 4)
- x – 3y = 6
c. y + 3 = -2(x + 1)
d. 2x – 5y = 10
e. y = -5
f. 3x + y = 5
14. Describe the transformations from the parent function for each equation:
- y = ½ x – 4b. y = -3x + 1c. y= -x
15. If the y-intercept of y = 3x – 2 is increased by 5 and the slope is doubled, what will be the new equation? What will be the effect on the graph?
Directions: Choose the best answer for each question.
16. Line A passes through the points (1,1) and (3,5), while Line B passes through (2,0) and (0,1). Which statement best describes lines A and B?
a. Line A is above Line Bc. Line A is parallel to Line B
b. Line A and Line B are collineard. Line A is perpendicular to Line B
17. Line P passes through the point (3,4) and is perpendicular to the line with the equation 3x + 2y = 8. What is the equation for Line P?
a. y = x + 4c. y = x +
b. y = x + d. y = x + 2
18. Which equation in standard form has a graph that passes through the point (-4, 2) and has a slope of ?
- 9x – 2y = 36c. 9x – 2y = -40
- 9x – 2y = 26d. 9x – 2y = -10
19. Linear function f(x) = x is graphed on a coordinate plane. The graph of a new line is formed by changing the slope of the original line to and the y-intercept to 4. Which statement about the relationship between the two graphs is true?
a. The graph of the new line is steeper than the graph of the original line, and the y-intercept has been translated down.
b. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up.
c. The graph of the new line is steeper than the graph of the original line, and the y-intercept has been translated up.
d. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated down.
20. Which equation has an x-intercept of -3 and a y-intercept of 9?
a. 4x - 2y = 6c. -2x + 3y = 18
b. -3x + 2y = 8d. 3x – y = -9
21. Which equation describes a line that is parallel to y = x + 1?
- 3x + 4y = 1c. -3y = 4x - 2
- 4y = 3x – 18d. y – 8 = (x – 2)
22. Which equations are equivalent?
- I and IIc. I, III, IV
- I and IIId. I, II, III, IV