# Graphing Lines 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.

2
Q

What are the three forms of a line?

A

slope-intercept, point-slope, and standard form

3
Q

What is the Point Slope Form?

A

y-y = m (x-x)

4
Q

What is the Slope Intercept Form?

A

y=mx+b

5
Q

What is the Standard Form?

A

Ax+By=C

6
Q

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

A

Point Slope

7
Q

y=mx+b what form?

A

slope intercept

8
Q

Ax+By=C What form?

A

Standard Form

9
Q

Why is it called “point-slope” form?

A

It has a hidden point (x,y) and a slope (m) in it

10
Q

Why is it called “slope-intercept” form?

A

It has a slope (m) and an intercept (b) in it

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

12
Q

How do you find the X-Intercept in Standard Form?

A

Use ( C over A, 0) to get the x intercept.

13
Q

How do you find the slope in Standard Form?

A

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

14
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, __).

15
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)

16
Q

What are the slopes of the diagonals of a square?

A

+1 and -1

17
Q

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

A

zero

18
Q

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

A

one

19
Q

what do you call something that goes straight up and down?

A

VERTICAL

20
Q

What dod you call something that goes from left to right?

A

HORIZONTAL (like looking along the horizon)

21
Q

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

A

(0,9)

22
Q

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

A

(9,0)

23
Q

the equation for the slope of the line is (if you have two points)

A

m = y-y / x-x

24
Q

People think of the slope as _____ over _____

A

RISE, RUN

25
Q

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

A

origin

26
Q

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

A

y=x

27
Q

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

A

y=-x

28
Q

What does the line y=4 look like?

A

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

29
Q

What does the line x=4 look like?

A

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

30
Q

How can you think about 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

31
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

32
Q

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

A

SLOPE INTERCEPT, (0,-5), 2/3

33
Q

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

A

STANDARD, (0,10)or(8,0), -5/4

34
Q

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

A

POINT SLOPE, (-8,7), 1/2

35
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

36
Q

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

A

WALK x then CLIMB y

37
Q

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

A

less steep

38
Q

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

A

steeper

39
Q

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

A

zero

40
Q

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

A

undefined (straight up and down)

41
Q

What does VERTICAL mean?

A

goes straight up and down

42
Q

What does HORIZONTAL mean?

A

goes from left to right

43
Q

What is the origin?

A

(0,0)

44
Q

WHat does the line y=0 look like?

A

it is the x axis (all of the points on the x axis have a y value of Zero

45
Q

What does the line x=0 look like?

A

it is the y axis (all of the points on the y axis have an x value of ZERO)

46
Q

What does the line y=x look like?

A

Perfect positive diagonal through origin (0,0)

47
Q

What does the line y= -x look like?

A

Perfect negative diagonal through origin (0,0)

48
Q

What is the equation of the x axis?

A

y=0

49
Q

Wat is the equation of the y axis?

A

x=0

50
Q

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

A

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

51
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

52
Q

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

A

Use algebra to rearrange it

53
Q

What form? y = 4x - 3

A

slope intercept

54
Q

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

A

point slope

55
Q

What form? 4x-2y=7

A

standard

56
Q

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

A

special form with a slope of 3 through the origin, or change to y=3x+0 SLOPE INTERCEPT (ZERO INTERCEPT). (0,0), 3

57
Q

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

A

special horizontal through (0,7), or change to y=0x+7 SLOPE INTERCEPT (ZERO SLOPE), (0,7), zero

58
Q

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

A

special none. vertical line. (9,0), undefined

59
Q

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

A

POINT SLOPE, (6,5), 4

60
Q

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

A

STANDARD, (0,2) or (-2,0), slope of 1

61
Q

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

A

SLOPE INTERCEPT, (0,2), 3

62
Q

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

A

SLOPE INTERCEPT, (0, -G), H

63
Q

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

A

POINT SLOPE, (-T, M), Z

64
Q

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

A

STANDARD, (0, H/R) or (H/P, 0), -P/R

65
Q

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

A

special horizontal. POINT SLOPE (ZERO SLOPE), (0,W), zero

66
Q

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

A

none, special vertical line, (B,0), undefined

67
Q

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

A

special slope intercept, the intercept is zero. Point (0,0), SLOPE (Q)

68
Q

How do you find the Y-Intercept when given Standard form?

A

Use (0, C over B) to get the y intercept and