Download Year 1 Unit 3 Functions, Slope and Equations of Lines

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Date:
Year 1 Unit 3 Functions, Slope and Equations of Lines
Matching
1. _______ Function
a. Any set of ordered pairs.
2. _______ Relation
b. A relation in which each input has only one output
3. _______ Linear Function
c. a(b + c) = ab + ac
4. _______ Non-Linear Function
d. the ratio of the change in the rise to the change in the run
5. _______ Domain
e. the value where a line crosses the x-axis
6. _______ Range
f. a graph that makes a straight line
7.________ Slope
g. the outputs of a function
8.________ x - intercept
h. a graph that makes another shape
9.________ y - intercept
i. the value where a graph crosses the y-axis
10._______Vertical Line Test
j. the inputs of a function
k. test used to determine if a graph is a function
11. Fill in the blanks with the most appropriate answer.
 When a line is decreasing from left to right, its slope is _______________________.
 When a line is horizontal, its slope is _____________________.
 When a line is vertical, its slope is ____________________.
 When a line is increasing from left to right, its slope is ________________________.
 Slope-intercept form is written ______________.
 In y=mx+b, the b represents the _______________.
Is each relationship a function? How do you know?
12. {(6, 3), (3, 6), (3, 3), (0, 1)
15.
x -4 -2 0 2
y 1 2 3 2
13.
14.
4
1
List the domain and range for each relation below.
16. {(1,1), (2,4), (0,3), (9,2)}
17.
domain:
y
domain:
x
range:
range:
Make a table and graph the following function.
18. y = x + 3
19. For f(x) = 3x – 7 find:
a. f(2)
b. f(-3)
c. f(-1/3)
Circle the solutions to the following functions.
20. y = x + 2
a. (0,2)
b. (-6, 8)
c. (2,4)
21. y = -5x + 1
b. (2, -11)
c. (-3, 15)
a. (0, 1)
Find the slope of the line that contains the given points. SHOW YOUR WORK!!
22. (-2, -1) and (-4, -3)
23. (0, -7) and (-3, 5)
24. (-2, 4) and (0, 4)
25. (6, -2) and (6, 5)
Write the equation in slope intercept form for the line using the given information.
26.
27.
28.
x -4 -2 0 2 4
y 0 2 4 6 8
29.
x -4 -2 0 6
y -7 -3 1 13
30. Write the equation of a line if the slope is -2 and the y-intercept is –5.
8
17
31. Write the equation of the line with slope 2 that passes through the point (3, 0).
32. Write the equation of the line with slope –¼ that passes through the point (-4, 8).
33. Write the equation of the line that passes through the points (-1, 7) and (2, -8).
34. Write the equation of the line that passes through the points (-1, 4) and (5, -2).
Find the coordinates of the x- and y-intercepts of the line, then graph the line.
35. 4x + 8y = -16
36.
–3x + 6y = 9
x-intercept: ____________
x-intercept: ____________
y-intercept: ____________
y-intercept: ____________
DIRECTIONS: rewrite the equation in slope-intercept form and find the slope an y-intercept for the line.
37. Find the slope and the y-intercept of the equation –2x + 3y = –12.
slope: ________y-intercept: _______
38. Find the slope and the y-intercept of the equation –x - 2y = 6.
slope: ________y-intercept: _______
Write the equation of a line through (-1, 4) if the line is:
41.horizontal
42. vertical
Answer the questions based on the following situation.
ABC garage charges $14 for an oil change plus $1.50 for each quart of new oil.
XYZ garage charges $20 for an oil change plus $0.50 for each quart of new oil.
42. Write an equation to represent the cost of an oil change at each garage.
ABC: ______________
XYZ: _____________
43. How much would an oil change cost at each garage if your car needs 4 quarts of new oil?
44. Sue spent $24 on an oil change at XYZ garage, how many quarts of oil did she need?
45. Sam needed the same amount of quarts as Sue needed in question #44. He went to ABC garage.
How much was his oil change?
46. Which garage has the better deal? Is that true for all circumstances?
47. Find the equation of the line you think best represents the average
time to brake at the given speed according to the graph.
a. S = 6x + 60
c. S = 6x – 60
b. S = -6x + 60
d. S = -6x - 60
48. Use your equation from #47 to predict how fast a driver is going if it
takes 6 seconds to brake.
49. Find the equation of the line you think best represents the average amount of money spent compared to the
time spent at the mall.
a. P = 5t + 25
c. P = 5t – 25
b. P = -5t + 25
d. P = -5t - 25
50. Use your equation from #49 to predict how much money you
would spend if you were at the mall 7 hours.
Money (dollars)
Hours in Mall vrs Money Spent
120
100
80
60
40
20
0
0
2
4
6
Tim e (hours)
8
10