Do the points in each set lie on the same line 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

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

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

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

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

Find the slope of the line that passes through each pair of points Question 7

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

Question 9 Write each equation in slope-intercept form. 6x + 9y = 27

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

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

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

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

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

The debate club needs $240. 00 to attend a debate tournament 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

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

Question 17 Do these tables show a constant rate of change? a. b. Time Distance 1 260 2 520 3 780 4 1040 x y -3 7.5 -1 2.5 2 -5 5 -12.5 Question 17

Suppose y varies directly with x and when y is 8, x is -4 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

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

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

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

You start a pet grooming service. You spend $30 on supplies 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

Question 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

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

Sometimes true. An example is y = 6x 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

Answers 7. m = 3 8. See next slide 9a. y = −2 3 x + 3; 9b. y = 7 3 x + 4 10a. 4;2 b. 4 4 5 ; -8 11a. y + 2 = 1 4 x b. y – 1 = -2x 12a. y = -2x + 7 b. y = - 2 7 x - 4 7 13a. y = - 1 2 x + 3.5 b. x = -7 14a. y = - 1 4 x + 1 4 b. x= 4 15a. 0.5x + 0.8y = 240 15b. 480; 300 16a. y = |x| + 3 b. y = |x + 2| 17a. no b. yes 18. y = -2x 19. m = -3 20. -4x + y = -3 21. Yes 22. y = 5x – 30 23a. parallel b. neither Answers

Question 8 Answer