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MONOMOY GEOMETRY > Graphing Linear Equations (all three forms) > Flashcards

Graphing Linear Equations (all three forms) Flashcards

1
Q

What is a linear equation?

A

It is a straight line (not a curve), and the x is not squared or cubed.

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2
Q

What are the three forms of a line?

A

slope-intercept, point-slope, standard

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3
Q

What is the point slope form?

A

y-y = m (x-x)

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4
Q

WHat is the slope intercept form?

A

y=mx+b

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5
Q

What is the standard form?

A

Ax+By=C

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6
Q

y-y=m(x-x) what form?

A

point slope

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7
Q

y=mx+b what form?

A

slope intercept

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8
Q

Ax+By=C What form?

A

standard

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9
Q

Why is it called “point-slope” form?

A

it has a hidden point and a slope in it

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10
Q

Why is it called “slope-intercept” form?

A

it has a slope and an intercept in it

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11
Q

How do you find the hidden point in point slope form? y-y=m(x-x)

A

to get your (x,y), take the opposite of the number next to the x to get your x, and take the opposite of the number next to the y to get your y

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12
Q

How do you find the points in Standard Form?

A

(0, __) to get the y intercept and (__,0) to get the x intercept.

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13
Q

How do you find the slope in Standard Form?

A

m = -A/B (opposite of A over B)

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14
Q

What is a trick to identify the correct form?

A

Look at the equal sign. What is to the left?
just a y ? then slope intercept
a y + or - something? then point slope
an X and a Y? then standard

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15
Q

How can you find the y intercept in any form?

A

You can always just plug a zero in for x and then solve for y. (0, __).

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16
Q

How can you find the x intercept in any form?

A

You can always just plug a zero in for y and then solve for x. (__ ,0)

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17
Q

What is a way to remember how to plot points like (-2,4) or (7, 8)

A

WALK x then CLIMB y

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18
Q

What are the slopes of the diagonals of a square?

A

+1 and -1

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19
Q

A slope of 2/3 is (steeper/less steep) than one.

A

less steep

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20
Q

A slope of -5/2 is (steeper/less steep) than negative one.

A

steeper

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21
Q

A slope of 1/10 is closer to (zero or one)

A

zero

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22
Q

A slope of 7/8 is closer to (zero or one)

A

one

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23
Q

A slope of 0.0001 is closer to (zero or one)

A

zero

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24
Q

A slope of 5 is closer to (one or undefined)

A

undefined (straight up and down)

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25
Q

If a line has a y intercept of 9, then the point _____ is on the line.

A

(0,9)

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26
Q

If a line has an x intercept of 9, then the point _____ is on the line.

A

(9,0)

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27
Q

If you are given two points, the equation for the slope of the line is

A

m = y-y / x-x

28
Q

People think of the slope as _____ over _____

A

RISE, RUN

29
Q

what form? y = 4x - 3

A

slope intercept

30
Q

what form? y - 3 = 2( x-8)

A

point slope

31
Q

what form? 4x-2y=7

A

standard

32
Q

What is the origin?

A

(0,0)

33
Q

What is the name of the point (0,0) ?

A

origin

34
Q

Name the FORM, name a POINT and name the SLOPE: y = 2/3 x - 5

A

form: SLOPE INTERCEPT
point: (0,-5)
slope: 2/3

35
Q

Name the FORM, name a POINT and name the SLOPE: 5x + 4y = 40

A

form: STANDARD,
point: (0,10)or(8,0),
slope: -5/4

36
Q

Name the FORM, name a POINT and name the SLOPE: y-7 = 1/2 (x+8)

A

form: POINT SLOPE,
point: (-8,7)
slope: 1/2

37
Q

Name the FORM, name a POINT and name the SLOPE: y = 3x

A

special form (through origin), or change to y=3x+0

form: SLOPE INTERCEPT (ZERO INTERCEPT).
point: (0,0)
slope: 3

38
Q

Name the FORM, name a POINT and name the SLOPE: y = 7

A

special forms (horizontal), or change to y=0x+7,

form: SLOPE INTERCEPT (ZERO SLOPE),
point: (0,7)
slope: zero

39
Q

Name the FORM, name a POINT and name the SLOPE: x = 9

A

form: special form. vertical line.
point: 9,0),
slope: undefined

40
Q

Name the FORM, name a POINT and name the SLOPE: y-5 = 4(x -6)

A

form: POINT SLOPE
point: (6,5)
slope: 4

41
Q

Name the FORM, name a POINT and name the SLOPE: 5x - 5y = -10

A

fprm: STANDARD,
point: (0,2) or (-2,0),
slope of 1

42
Q

Name the FORM, name a POINT and name the SLOPE: y = 3x + 2

A

form: SLOPE INTERCEPT,
point: (0,2),
slope: 3

43
Q

Name the FORM, name a POINT and name the SLOPE: y = Hx - G

A

form: SLOPE INTERCEPT,
point: (0, -G),
slope: H

44
Q

Name the FORM, name a POINT and name the SLOPE: y - M = Z (x + T)

A

form: POINT SLOPE,
point: (-T, M),
slope: Z

45
Q

Name the FORM, name a POINT and name the SLOPE: Px + Ry = H

A

form: STANDARD,
point: (0, H/R) or (H/P, 0),
slope: -P/R

46
Q

Name the FORM, name a POINT and name the SLOPE: y = W

A

special form, horizontal, or change to y=0x+w,

form: POINT SLOPE (ZERO SLOPE),
point: (0,W),
slope: zero

47
Q

Name the FORM, name a POINT and name the SLOPE: x = B

A

form: special form, vertical line,
point: (B,0),
slope: undefined

48
Q

Name the FORM, name a POINT and name the SLOPE: y = Qx

A

special form, or change to y=Qx+0,
form: slope intercept, the intercept is zero.
Point (0,0),
SLOPE (Q)

49
Q

WHat does the line y=0 look like?

A

it is the x axis

50
Q

What does the line x=0 look like?

A

it is the y axis

51
Q

What does the line y=x look like?

A

perfect positive diagonal through origin (0,0)

52
Q

What does the line y= -x look like?

A

perfect negative diagonal through origin

53
Q

What is the equation of the x axis?

A

y=0

54
Q

Wat is the equation of the y axis?

A

x=0

55
Q

What is the equation of a perfect positive diagonal going through tjhe origin?

A

y=x

56
Q

WHat is the equation of a perfect negative diagonal going through the origin?

A

y=-x

57
Q

What does the line y=4 look like?

A

horizontal (L to R) line through (0,4). up 4.

58
Q

What does the line x=4 look like?

A

vertical (up and down) line through (4,0), to the right 4.

59
Q

What does the line y = 1/2 x look like?

A

through origin (0,0) with slope of 1/2

60
Q

Why are the A, B and C capital letters in Ax+By=C?

A

They have to be INTEGERS (whole numbers). This means that you won’t see 1/2x + 4/5y = 1/3. The A and B and C have to be integers like 4x-2y=9

61
Q

What if a linear equation is not in one of the three forms?

A

use algebra to rearrange it

62
Q

How can you think of the line x=5 to remember what it looks like?

A

It is all of the points that have an x value of five… so (5, 0), (5, 1), (5, 2), (5, 3), etc… straight up and down

63
Q

How can you think about the line y=8 to remember what it looks like?

A

It is all of the points that have a y value of eight. So (0,8), (1,8), (2,8) ,(3,8), (4,8), (5,8)… All have a height of 8. Horizontal line up 8

64
Q

How can you think of the points on the line y=x to remember what it looks like?

A

It is all of the points whose x and y are the same. (4,4), (10,10), (-5,-5), etc..

65
Q

when you graph a line.. what are you actually graphing?

A

THE SOLUTION! your are graphing all of the (x,y) partners that make the equation TRUE!!!

MONOMOY GEOMETRY (1 decks)

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