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2020 BC BLOCK ALGEBRA 2 > DECK 1: ALGEBRA 1 TOPICS > Flashcards

DECK 1: ALGEBRA 1 TOPICS Flashcards

1
Q

What is your favorite class?

A

ALGEBRA 2

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2
Q

What is the slope of a line?

A

it is the steepness

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3
Q

How do a lot of people think about the slope (the slope)?

A

rise/run… or change in y / change in x

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4
Q

what is the cartesian plane?

A

it is the thing we plot points on with the x y axis.. named after RENE DESCARTES, french philosopher and mathematician.

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5
Q

If you draw a square with the diagonals as an X, what is the slope of the diagonal that goes from bottom left to upper right corner?

A

1

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6
Q

If you draw a square with the diagonals as an X, what is the slope of the diagonal that goes from top left to the bottom right corner?

A

-1

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7
Q

If a slope of zero is 0 degrees, what is a slope of 1?

A

45 degrees uphill (traveling L to R)

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8
Q

if a slope of zero is 0 degrees, what is a slope of -1?

A

45 degrees downhill (traveling L to R)

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9
Q

What does “horizontal” mean?

A

left to right.. like a floor or table top

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10
Q

What does “vertical? mean?

A

up and down

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11
Q

What are the slopes of the diagonals of a square?

A

+1 going up L to R, and -1 going down from L to ROW

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12
Q

How can you think of a slope of 1 or -1?

A

If you draw a square, think of the diagonals.. 45 degrees!

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13
Q

What is an interesting fact about slopes between -1 and +1?

A

HALF OF ALL POSSIBLE SLOPES ARE BETWEEN -1 and +1 (and they are perpendicular)

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14
Q

What is the slope of a flat horizontal surface?

A

ZERO

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15
Q

What is the slope of a horizontal line?

A

ZERO

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16
Q

What is the slope of a vertical line?

A

undefined

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17
Q

what is the slope of a line that goes straight up and down?

A

undefined

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18
Q

the number 0/5 is equal to :

A

zero. 0

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19
Q

the number 5/0 is equal to :

A

undefined

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20
Q

Why can’t you divide by zero? (why can zero be in the top and not the bottom?)

A

10/2 asks “how many times do you add 2 to itself to get to 10?” the answer is 5. 10/0 asks “how many times do you add 0 to istelf to get to 10?” the answer is there is no answer. undefined

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21
Q

What is the x intercept of a line? (what are the coordinates?)

A

Where the line crosses the horizontal axis, the x axis. The coordinates are ( X, 0 )

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22
Q

What is the y intercept of a line? (what are the coordinates?)

A

Where the line crosses the vertical axis, the y axis. The coordinates are ( 0, Y )

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23
Q

what are the coordinates of a point?

A

(x,y), the x and y value.

24
Q

What is the y coordinate for all x-intercepts?

A

zero. all x intercepts have a height of zero because they are on the x axis.

25
Q

What is the x coordinate for all y-intercepts?

A

zero. all y intercepts are in the middle, not left or right, because they are on the y axis.

26
Q

What do you know about all X-intercepts?

A

(x,0) they have a y coordinate of ZERO

27
Q

What do you know about all Y intercepts?

A

(0,y) they have an x coordninate of ZERO

28
Q

Parallel lines have ______ slopes, or slopes

A

the same

29
Q

Perpendicular lines have _____ slopes, or slopes

A

OPPOSITE SIGN AND RECIPROCAL

30
Q

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

A

2/3 and perp -3/2

31
Q

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

A

-5 and perp 1/5

32
Q

How can you tell if the point (5, -3) is a solution to a linear equation?

A

If it “works.” Sub 5 in for the X and -3 in for the Y. Simplify. If the statement is true, then it is a solution. If it is a solution, then it is on the line.

33
Q

How can you tell if the point (5, -3) is on a line if you are given the equation?

A

If it “works.” Sub 5 in for the X and -3 in for the Y. Simplify. If the statement is true, then it is a solution. If it is a solution, then it is on the line.

34
Q

What is the equation of the x axis?

A

y=0

35
Q

What is the equation of the y axis?

A

x=0

36
Q

What is the equation of a vertical line that goes through the x axis at 7? How can you think of that line to help make sense of it?

A

x = 7. You can think “all of the points on this line have an x value of 7, so you are a solution as long as your x=7.

37
Q

What is the eqution of a horizontal line that goes througyh the y axis at 8? How can you think about it to help you?

A

y = 8. Since y is the height, you can think of it as all of the points that have a height of 8. Also, you can think of it as all of the points that have a y value of 8, so you are a solution if your y value is 8.

38
Q

If an x intercept is 455, what point is on the line?

A

(455, 0)

39
Q

If a y intercept is 990, what point is on the line?

A

(0, 990)

40
Q

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

A

Show that, when you plug the point in, you get a true mathematical statement.

41
Q

what does a slope of zero look like?

A

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

42
Q

what does a slope that is undefined look like?

A

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

43
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

44
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).

45
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)

46
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)

47
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

48
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

49
Q

describe what the line y=12 looks like

A

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

50
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

51
Q

what is the origin?

A

the point (0,0)

52
Q

what is an undefined slope look like?

A

up and down (vert)

53
Q

what does a zero slope look like?

A

left to right (horiz)

54
Q

what is the point (0,0) called?

A

the origin

55
Q

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

A

the cartesian plane

2020 BC BLOCK ALGEBRA 2 (5 decks)

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