Download Unit 20 GRE 502 503 Worksheet

GRE 502 & GRE 503 Work Sheet CRS SKILL GRE 502 GRE 503 Period____________ Name_________________________________________ LEVEL Level 1 – ALL students must attain mastery at this level DESCRIPTION GRE 401 Locate points on a coordinate plane GRE 403 Exhibit knowledge of slope Level 2 – MOST students will GRE 502 Determine the slope of a line from points or attain mastery of the focus skill in equations isolation. GRE 503 Match linear graphs with their equations Level 3 – SOME students will attain mastery of focus skill with other skills Level 4 – SOME students will attain mastery of focus topics covered in a more abstract way Level 5 – FEW students will GRE 601 Interpret and use information from graphs attain mastery of the extension in the coordinate plane skill. GRE 604 Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point Level 1 1. Plot the following:
6
A (-2, 5)
B (3, 6)
4
C (-4, -5)
2
D (1, -3)
E (0, 4)
F (-6, 0)
-5
5
-2
-4
-6
1 2. Write the coordinates of the rectangle in the space below: A: A B: D C: D: B 3. Emma was driving a car at a constant speed on the New York State Thruway. She noticed that after driving for 1 hour she had 12 gallons of gas left. Then after driving for a total of 3 hours, she had 8 gallons of gas left. a. Express the information given in this problem as a set of two-­‐ordered pairs. b. At what rate is the gas in Jesse’s car decreasing? Include units in your answer. c. How long, after she started driving, will Emma run out of gasoline? 4. Laura weighed 130 lbs. in 1986 and weighed 175 lbs. in 2007. a. Express the given information in this problem as two-­‐ordered pairs. b. At what rate is this person’s weight increasing each year? Include units in your answer. c. If this person’s weight gain continues at this same rate, in what year will they weigh 200 lbs.? 2 C 5. Mrs. Brenneman frequently lends her student’s pencils during class. Many of the days, her students do not return them. The number of pencils she was lending out seemed to increase so she started to make a chart with how many pencils she lends. Week Number Total number of pencils lent out a. Find the rate of change in number of pencils Mrs. Brenneman lent between 2 25 weeks 2 and 4. 4 55 b. Find the rate of change in number of pencils Mrs. Brenneman lent between weeks 6 and 8. 6 95 8 145 c. Does it appear that the number of pencils being lent out per week is increasing or decreasing? 6. The table below shows the cost of using a computer at an internet café’ for a given amount of time. Time (hours) 2 4 6 Cost (dollars) 7 14 21 a. Write two ordered pairs from the data above. b. Find the rate of change for cost per time. 7. Make a drawing of the following slopes. 5
a)
7
-2
b)
7
1
c)
10
1
d)
-5
-2
e)
9
5
f)
2
3 12
8. Plot the points (2,2) and (5,8) on the grid below. What is the slope between these two points? 10
8
9. Plot the point (4,6) on the grid above. What is the slope from (2,2) to (4,6)? 6
10. Plot (5,2) and (8,8) on the grid above. What it the slope between these two points? What do you notice about this slope and the slope from (2,2) to (5,8)? 4
2
11. Determine the slope of each the following equation: a) y = 5x − 2
5
10
b) y = 8 − 2x
−2
−6
c) y =
x+
3
7
d) y =
−1 −2
+
x
4
7
Level 2 12. Graph each of the following: y = −4x + 2
y = −5 +
3
x 7
4 13. Write the equation of each of the following. A) C) B) D) 14. Graph and label each of the following equations on the graph below: 10
1
a) y = x − 2
3
8
6
−2
b) y =
x+4
3
4
2
c) y = 3x
d) y = −5
e) x=8
-10
-5
5
10
-2
-4
-6
-8
-10
5 15. Find the slope of the line that passes through the following points: (6, -­‐7) and (2, 3) 16. Find the slope of the line that passes through the following points: (7, 4) and (-­‐7, -­‐3) 17. Find a Point-­‐Slope equation for a line containing the given point and having the given slope. a. (7, 0), m = 4 b. (5, -­‐1), m =-­‐6 c. (-­‐5, -­‐6), m = 2 18. Write the equation of each line below, using the point-­‐slope form. a. b. 6
6
4
4
2
2
-5
5
-5
5
-2
-2
-4
-4
-6
-6
6 19. The lines below are given in standard form. Find the x-­‐ and y-­‐intercepts, a third point and then graph the line. a) 3x + 2y = – 6 b) 2x – 4y = 4 c) –5x + 2y = 10 x-­‐intercept=_________ x-­‐intercept=_________ x-­‐intercept=_________ y-­‐intercept =___________ y-­‐intercept =___________ y-­‐intercept =___________ another point _________ another point________ another point________ 20. Graph and label the following two lines. Write the coordinates of their intersection point. x = −5 y = 4 7 Level 3 21. Graph the following three lines and find the area of the triangle enclosed by them. x = 5 y = −3 y = 2x −1 A: Photographer
For each ‘shoot’ a photographer charges a fixed fee for
expenses, then a fixed 555amount for each hour (or part of
an hour.)
x = the time a ‘shoot’ takes in hours.
y = the total amount the photographer charges.
B: Football
In a football league, each team plays all other teams twice.
x = the number of teams.
y = the number of games played by one team.
A: Candle
Each hour a candle burns down the same amount.
x = the number of hours that have elapsed.
y = the height of the candle in inches. D: Saving up
Tanya saves a fixed amount each week until she has enough
money in the bank to buy a coat.
x = the amount saved each week.
y = the time that it takes Tanya to save enough for the coat.
8 Level 4 22.
Karen left her house and drove at a constant speed to a conference in another state. She picked up Annathea along the way. Two hours after picking up Annathea, they were 140 miles from Karen’s house, and 5 hours after picking up Annathea, they were 344 miles from Karen’s house. How far from her house was Karen when she picked up Annathea? 23. The United States Bureau of Census predicts that the population of Florida will be about 21.15 million in 2020 and then will increase by about 0.24 million people unit 2030. Write an equation that predicts the population of Florida (in millions) in terms of x, the number of years after 2020. 24. A home security company charges new customers $155 for the installation of security equipment and a monthly fee of $40. a. Write an equation that represents the total cost for x months of service. b. Graph the equation. c. What is the cost for a year of service? C
o
s
t
Number of Months
9 Level 5 25.
Find the slope of a line parallel to and the slope of a line that is perpendicular to the graph of each of the following equations. Equation y=
1
x − 9 3
Slope of a line parallel Slope of a line perpendicular y = 2+
3
x 8
8x-­‐6y=24 y + 5 = 7(x − 9) 26. Write the equation in slope-­‐intercept form for the line that contains the point (8,-­‐1) and is perpendicular to the graph of y = 7x + 3. 25. Create a rough sketch and then write the equation of the line that fits each description: a. Parallel to the x-­‐axis passing through (3, 2) b. Parallel to the y-­‐axis passing through (−4, 3) 26. Which of the following represents the equation of the x-­‐axis? a. x=1 b. y=0 c. y=1 d. x=0 10 27. Which of the following represents the equation of a line that is parallel to the y-­‐axis and passes through the point (1, 4)? a. x=1 b. y=4 Mixed Review 28. Solve each of the following: a. p−1=5p+3p−8 b. p−4=−90+ 3p c. 12=−4(−6x−3) c. a2 −144=0 29. What is 12% of 17.5? 30. What is 59% of 14 m? 31. What is the percent change from 117 minutes to 91 minutes? 32. Solve the following quadratic equation by factoring. a. b2 +b−30=0 b. n2 +6n−7=0 11