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Question 1

Do the points in each set lie on the same line? Show your work to explain your answer. A(1,3), B(4,2), C(-2,4). Question 1. Open-ended: Find two points that lie on a line with a slope of -3. Question 2.

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Question 1

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  1. Do the points in each set lie on the same line? Show your work to explain your answer. A(1,3), B(4,2), C(-2,4) Question 1

  2. Open-ended: Find two points that lie on a line with a slope of -3. Question 2

  3. Is it always, sometimes, or never true that an equation that is in slope-intercept form represents a direct variation? Support with an example. Question 3

  4. Write an equation of a line that passes through (-2,5) Question 4

  5. A student says the equation y = 4x + 1 can be written in standard form as 4x – y = 1. Describe and correct the student’s error. Question 5

  6. True of False: The rate of change for a vertical line is zero. Question 6

  7. Find the slope of the line that passes through each pair of points. (−3, −1), (−1, 5) Question 7

  8. Graph the equation. x + 2y = 6 Question 8

  9. Write each equation in slope-intercept form. • 6x + 9y = 27 • 7x = 3y − 12 Question 9

  10. Find the x- and y-intercepts of the graph of each equation. • 6x + 12y = 24 • −5x + 3y = −24 Question 10

  11. Write an equation in point-slope form for the line that has the given slope m and that passes through the given point. • m = ¼; (0, -2) • m = -2; (0,1) Question 11

  12. Write an equation in slope-intercept form for the line that passes through the given points. • (2, 3), (1, 5) • (5, −2), ( −16, 4) Question 12

  13. Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the given line. • (-3, 5); y = -1/2x + 4 • ( −7, 3); x = 4 Question 13

  14. Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the given line. • (5, −1); y = 4x −7 • (4, −2); y = 3 Question 14

  15. The debate club needs $240.00 to attend a debate tournament. The club decides to sell cups of iced tea and lemonade at baseball games. Iced tea will be sold for $.50 per cup and lemonade will be sold for $.80 per cup. a. Write an equation to find how many cups of each beverage must be sold to raise $240.00. b. Graph the equation. What are the x- and y -intercepts? Question 15

  16. Write an equation for each translation of y = |x|. • 3 units up • left 2 units Question 16

  17. Do these tables show a constant rate of change? a. b. Question 17

  18. Suppose y varies directly with x and when y is 8, x is -4. Write a direct variation equation that relates to x and y. Question 18

  19. What is the slope of this equation? 12x + 4y = 24? Question 19

  20. Write this equation in standard form. y = 4x – 3 Question 20

  21. Does this represent a direct variation? 2x + 3y = 0 (hint: solve for y) Question 21

  22. You start a pet grooming service. You spend $30 on supplies. You plan to charge $5 to groom each pet. Write an equation to relate you profit y to the number of pets x you groom. Question 22

  23. Are these two lines parallel, perpendicular or neither? a. y = 6x + 2 and 18x – 3y = 15 b. 25. y = 4x – 2 and –x + 4y = 0 Question 23

  24. Answer: yes Explanation: Graph the points on graph paper to see if it makes a line or find the slope between the points. • Sample answer: y = -3x + 1 Explanation: to make a correct answer, start with y = mx+b. Think of a slope, a y-coordinate, and an x coordinate. In my sample, I came up with -3 for the slope, 0 for x and 1 for y. Substitute y, m and x into y = mx + b and solve for b. Then make a general equation. My equation looked like 1 = -3(0) + b. The y-intercept is 1. Answers

  25. Sometimes true. An example is y = 6x. An example that is incorrect is y = 2x + 8. • An example is y = 3x + 11. This problem is similar Question 2. Create a slope and substitute x, y and m into y = mx + b and solve for b. • The student changed the sign on 4x and on y. • False; the slope is undefined. Answers

  26. Answers

  27. Question 8 Answer

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