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 2

Open-ended:

Find two points that lie on a line with a slope of -3.

Question 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 4

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

Question 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 6

True of False:

The rate of change for a vertical line is zero.

Question 7

Find the slope of the line that passes through each pair of points.

(−3, −1), (−1, 5)

Question 8

Graph the equation.

x + 2y = 6

Question 9

Write each equation in slope-intercept form.

a. 6x + 9y = 27

b. 7x = 3y − 12

Question 10

Find the x- and y-intercepts of the graph of each equation.

a. 6x + 12y = 24

b. −5x + 3y = −24

Question 11

Write an equation in point-slope form for the line that has the given slope m and that passes through the given point.

a. m = ¼; (0, -2)

b. m = -2; (0,1)

Question 12

Write an equation in slope-intercept form for the line that passes through the given points.

a. (2, 3), (1, 5)

b. (5, −2), ( −16, 4)

Question 13

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the given line.

a. (-3, 5); y = -1/2x + 4

b. ( −7, 3); x = 4

Question 14

Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the given line.

a. (5, −1); y = 4x − 7

b. (4, −2); y = 3

Question 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 16

Write an equation for each translation of y = |x|.

a. 3 units up

b. left 2 units

Question 17

Do these tables show a constant rate of change?

a. b.x y-3 7.5-1 2.52 -55 -12.5

Time Distance

1 2602 5203 7804 1040

Question 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 19

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

Question 20

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

Question 21

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

Question 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 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

Answers

1. Answer: yes

Explanation: Graph the points on graph paper to see if it makes a line or find the slope between the points.

2. 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

3. Sometimes true. An example is y = 6x. An example that is incorrect is y = 2x + 8.

4. 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.

5. The student changed the sign on 4x and on y.

6. False; the slope is undefined.

Answers

7. m = 3 8. See next slide

9a. y = x + 3; 9b. y = x + 4 10a. 4;2 b. 4; -8

11a. y + 2 = x b. y – 1 = -2x 12a. y = -2x + 7 b. y = - x -

13a. y = - x + 3.5 b. x = -7 14a. y = - x + 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

Question 8 Answer