DECK 3: Advanced Linear Concepts Flashcards Preview

2021 ALGEBRA 2 CONCEPTS AND VOCABULARY > DECK 3: Advanced Linear Concepts > Flashcards

Flashcards in DECK 3: Advanced Linear Concepts Deck (86)
1
Q

How do you show that a point lies on a line?

A

Show that, when you plug coordinates in for x and y in the function, you get a true mathematical statement.

2
Q

What happens if you plug the coordinates of point (x,y) that is NOT on the line in for x and y in a function?

A

It will make a FALSE statement

3
Q

How do you know if a graph will go through the origin?

A

If you can plug in the coordinates (0,0) in for x and y and get a true statement.

4
Q

What does it mean to “SOLVE” an equation?

A

Find values that make the equation true

5
Q

The graph of an equation is the set of all of the points, (x,y) that _____

A

will make the equation true when plugged in

6
Q

what does a slope of zero look like?

A

horizontal, flat from left to right. The x axis has a slope of zero.

7
Q

what does a slope that is undefined look like?

A

vertical, straight up and down. The y axis has a slope of zero.

8
Q

how can you think of the points on the line y=x to help you graph it?

A

all of the x values are equal to all of the y values.. so (2,2), (3,3), (5,5), (-100,-100) are all in the solution set and on the line

9
Q

How can you think of the points on the line y=-x to help you graph it?

A

the x values are opposite the y values… so (2, -2) and (-2, 2) and (-107, 107).

10
Q

How can you think of points on the lone y=5 to help you graph it?

A

all of the points on the cartesian plane with a y value of 5… (2,5), (9,5), (-200,5)

11
Q

How can you think of the line x=6 to help you graph it?

A

all of the points on the cartesian plane with an x value of 6: (6, 0), (6, -3), (6, 24.3), (6, -2000)

12
Q

Describe what the line y=x looks line

A

positive diagonal line from bottom left to upper right, slope of 1, through the origin

13
Q

Describe what the line y=-x looks like

A

negative diagonal line from top left to bottom right, slope of -1, through the origin

14
Q

describe what the line y=12 looks like

A

horizontal, from left to right, through (0,12)

15
Q

describe what the line x=-8 looks like

A

vertical, straight up and down, through the point (-8,0) on the x axis. undefined slope

16
Q

what is the origin?

A

the point (0,0)

17
Q

what does an undefined slope look like?

A

up and down (vert)

18
Q

what does a zero slope look like?

A

left to right (horiz)

19
Q

what is the point (0,0) called?

A

the origin

20
Q

what is the XY axis graph thing we plot lines and points on called?

A

the cartesian plane

21
Q

how can you think of the points on the line y=x to help you graph it?

A

the x and y are equal. so (2,2), (3,3), (5,5), (-100,-100) are all in the solution set and on the line

22
Q

How can you think of the points on the line y=-x to help you graph it?

A

the x and y are opposites. so (2, -2) and (-2, 2) and (-107, 107).

23
Q

How can you think of points on the line y=5 to help you graph it?

A

all of the points on the cartesian plane with a y value of 5. (2,5), (9,5), (-200,5)

24
Q

How can you think of the line x=6 to help you graph it?

A

all of the points on the cartesian plane with an x value of 6: (6, 0), (6, -3), (6, 24.3), (6, -2000)

25
Q

How do we write equation of horizontal lines?

A

y=___

26
Q

How do we write equations of vertical lines?

A

x= ____

27
Q

How do you quickly graph slope intercept form?

A

plot the given y intercept (0,b) and label, then use the slope to sketch a line through it.

28
Q

How do you quickly graph point slope form?

A

plot the given point (x,y) and label, then use the slope to sketch a line through it. Remember the OPPOSITES

29
Q

How do you quickly graph when in standard linear form?

A

Find the zeros. Cover the x term to find y intercept (0,y), cover the y term to find the x intercept (x,0).

30
Q

How would you graph

y= 1/2x + 7

A

plot (0,7) and sketch a line with a slope of 1/2 through it

31
Q

How would you graph

y-10=2(x+4)

A

plot (-4, 10) and sketch a line with a slope of 2 through it

32
Q

How woudl you graph

2x+5y=20

A

cover 2x to find that y-int is 4 (0,4), cover the 5y to find that x-int is (10,0)

33
Q

y= 1/3x -5

What form and what is the y-intercept?

A

this equation is in slope-intercept form and the y intercept is (0, -5)

34
Q

y= 1/3x -5

Name the form and name a point on the line

A

This is equation is in slope intercept form and a point is (0, -5)

35
Q

y= 1/3x -5

Name the form and find the slope.

A

This is equation is in slope intercept form and the slope is 1/3

36
Q

3x+4y=24

Name the form and name a point on the line

A

This is equation is in standard form and a point is (0, 6) or (8, 0)

37
Q

3x+4y=24

Name the form and the Y intercept:

A

This is equation is in standard form and the y intercept is (0, 6). You plug zero in for x and solve for y.

38
Q

3x+4y=24 Name the form and the X intercept:

A

This is equation is in standard form and the x intercept is (8,0). Plug zero in for y and solve for x.

39
Q

y-5=3(x+2)

Name the form and name a point on the line

A

This is equation is in point slope form and a point is ( -2, 5)

40
Q

y-5=3(x+2)

Name the form and find the slope.

A

This is equation is in point slope form and the slope is 3

41
Q

y-5=3(x+2)

Is the origin (0,0) on this line?

How do you know?

A

This is equation is in point slope form and if you plug (0,0) in you get -5= 3(2) which is not true, so the origin is not on the line. It is not a solution.

42
Q

y+7=1/3 (x-10)

Name the form and name a point on the line

A

This is equation is in point slope form and a point is (10, -7).

43
Q

y+7=1/3 (x-10)

Name the form and find the slope.

A

This is equation is in point slope form and the slope is 1/3

44
Q

y+5=1/2 (x+10)

Is the origin on this line?

How do you know?

A

This is equation is in point slope form and to check to see if the origin is on the line, you have to see if it is a solution. Plugging in (0,0) for x and y gives 5 = 1/2 (10) which is true, since (0,0) is a solution, It is indeed on the line.

45
Q

y= 1/2 x

What form and what is the y-intercept?

A

This is equation is in slope intercept form [y = 1/2x + 0] nd the y intercept is (0,0), the origin

46
Q

y= 1/2 x

Name the form and find the slope.

A

This is equation is in slope intercept form and the slope is 1/2.

47
Q

y= 1/2 x

Is the origin on this line? How do you know?

A

This is equation is in slope intercept form form and if you plug in (0,0) for (x,y) you get 0=1/2(0) which is true. The line goes through the origin.

48
Q

y= 1/2 x

Find the y coordinate for this point on the line: (10, ___)

A

Plug in 10 for x to get y= 1/2 (10) and you get y=5. The point (10, 5) is on the line

49
Q

x - y = 10 Name the form and name a point on the line.

A

This is equation is in Standard form and the point (0, -10) or (10, 0) is on the line. You can also pick any (x,y) such that the x is 10 more than the y, so (50, 40) works.

50
Q

x - y = 10

Name the form and find the y intercept.

A

This is equation is in standard form and plug 0 in for x to solve for y. (0, -10)

51
Q

x - y = 10

Name the form and find the x intercept.

A

This is equation is in standard form and plug 0 in for y and then solve for x. (10, 0)

52
Q

y+3 = -2(x-8)

Name the form and name a point on the line

A

This is equation is in point slope form and a point on the line is (8,-3)

53
Q

y+3 = -2(x-8)

Name the form and find the slope.

A

This is equation is in point slope form and the slope is -2

54
Q

y=x NAME 3 POINTS ON THE LINE

A

all points where x and y are equal. (5, 5), (0,0), (-2,-2)

55
Q

x=5

NAME 3 POINTS ON THE LINE

A

all points where x value is 5. (5,8), (5,0), (5,10000)

56
Q

y= -3 NAME 3 POINTS ON THE LINE

A

all points where y value is -3. (6,-3), (45, -3), (0, -3),

57
Q

y=-x NAME 3 POINTS ON THE LINE

A

all points where x and y are opposites. (5, -5), (-22, 22), (0,0), (48, -48)

58
Q

y= x

What is the slope?

A

1

59
Q

y = -x What is the slope?

A

-1

60
Q

y = 4

What is the slope?

A

0

61
Q

x = -3 What is the slope?

A

undefined

62
Q

x = 0 What is the slope?

A

undefined

63
Q

y = 0

What is the slope?

A

0

64
Q

x = 0

What special line is this?

A

this is the equation of the Y axis. All of the points have an x value of zero. Vertical line through (0,0) with undefined slope.

65
Q

y = 0

What special line is this?

A

This is the equation of the X axis. All of the points that have a y value of zero. A horizontal line through (0,0) with a slope of zero.

66
Q

x = 0 name 3 points on the line

A

any points with an x of zero (0, 6), (0, -9), (0, 0) These are all on the y axis.

67
Q

y = 0 name 3 points on the line

A

any points with a y coordinate of zero (9,0), (-300, 0), (0, 0) these are all on the x axis.

68
Q

Parallel lines have ______ slopes

A

the same

69
Q

Perpendicular lines have _____ slopes

A

OPPOSITE SIGN AND RECIPROCAL: change sign and flip it!!

70
Q

If one line has a slope of 2/3 and an other line has a slope of 2/3 then we can say these lines are ______

A

parallel

71
Q

If one line has a slope of -2/5 and the other has a slope of 2/5, then the lines are _____

A

perpendicular

72
Q

what are lines called that go in the same direction?

A

parallel

73
Q

what are lines called that cross eachoter at 90 degrees (right angle?)

A

perpendicular

74
Q

If a line as a slope of 2/3, then any line parallel to it will have a slope of __

A

2/3

75
Q

If a line as a slope of -5, then any line parallel to it will have a slope of ___

A

-5

76
Q

If a line has a slope of zero, all parallel lines will have a slope of ___

A

zero

77
Q

If a line has a slope of zero, all perpendicular lines will have a slope of ___

A

undefined

78
Q

If a line has a slope that is undefined, all parallel lines will have a slope of ___

A

undefined

79
Q

If a line has a slope that is undefined, all perpendicular lines will have a slope of ___

A

zero

80
Q

If a line has a slope of 3/5 , then any line perpendicular to it will have a slope of ____

A

5/3

81
Q

If a line has a slope of -3, then any line perpendicular to it will have a slope of ___.

A

1/3

82
Q

If you are given two points and need to find the equation of a line, how do you do it?

A

First, find the slope using m=(y-y)/(x-x), then use that slope and EITHER OF THE POINTS. Put it in point slope form.

83
Q

What is the equation of a vertical line passing through (6,5)?

A

x=6

84
Q

What is the equation of a horizontal line passing through (6, 5)?

A

y = 5

85
Q

What is the equation of the vertical line passing through (-8, 12.6) ?

A

x = -8

86
Q

What is the equation of the horizontal line passing through (-8, 12.6)

A

y = 12.6