Date post: | 29-Jan-2016 |
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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 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