Question

help!

Answer 1

@jim_thompson5910

Answer 2

which two points are on this line?

Answer 3

um, 2?

Answer 4

a point is an ordered pair (x,y)

Answer 5

which ordered pairs do you see on the table?

Answer 6

right, so 2,2

Answer 7

yes (2,2)

Answer 8

use parenthesis whenever you're talking about ordered pairs

Answer 9

what's another?

Answer 10

(4,5)?

Answer 11

?

Answer 12

good, so we have (2,2) and (4,5) as our two points

Answer 13

what is the slope of the line through those two points?

Answer 14

um, idk :(

Answer 15

do you know the slope formula?

Answer 16

no

Answer 17

slope formula

\[\Large m = \frac{y_2 - y_1}{x_2 - x_1}\]

Answer 18

does that formula look familiar?

Answer 19

no @jim_thompson5910

Answer 20

so what you do is subtract the y values first

Answer 21

looking at (2,2) and (4,5)
what are the y values here?

Answer 22

hint: (x,y)

Answer 23

(2,4)?

Answer 24

it's the second value of any ordered pair

Answer 25

so the y values in (2,2) and (4,5) are _____ and ______

Answer 26

2,5?

Answer 27

yes, 2 and 5 are the two y values

Answer 28

let's subtract them

(second y value) - (first y value) = 5 - 2 = 3

so the change in y is 3

Answer 29

what's the change in x? subtract the x values to find out

Answer 30

so i do: 4-2=4?

Answer 31

4-2 is not 4 though

Answer 32

sorry i meant 2

Answer 33

yes 4-2 = 2

Answer 34

change in y = 3
change in x = 2

Answer 35

slope = rise/run = (change in y)/(change in x) = 3/2

so the slope is 3/2

Answer 36

since the slope is 3/2, we can eliminate choice D

why? because choice D has a slope of 3 and not 3/2

Answer 37

A,B,C all have slope of 3/2

Answer 38

ok....

Answer 39

the slope is the number in front of the x

Answer 40

ok..

Answer 41

slope = m = 3/2

y = mx+b will turn into y = (3/2)*x + b

Answer 42

now let's replace x and y with one of the ordered pairs, say (x,y) = (2,2)

so
y = (3/2)*x + b
turns into
2 = (3/2)*2 + b

making sense so far?

Answer 43

yes!

Answer 44

what is (3/2)*2 equal to?

Answer 45

3

Answer 46

good

Answer 47

2 = (3/2)*2 + b
turns into
2 = 3 + b

Answer 48

looking at the equation 2 = 3 + b, what is the value of b?

Answer 49

um, idk

Answer 50

b+3 = 2

to solve for b, subtract 3 from both sides

Answer 51

-1

Answer 52

yep, so the final answer is y = (3/2)x - 1

Answer 53

ok! next :)

Answer 54

are you able to determine a point that lies on that line?

Answer 55

hint: look at the grid lines

Answer 56

0?

Answer 57

points are ordered pairs (x,y)

Answer 58

for instance, (0,4) is one point on the line. Do you see how/why?

Answer 59

no

Answer 60

start where the x and y axis meet. This point is the origin (0,0)

Answer 61

then go up 4 units to land on (0,4) which is where the line crosses the y axis

Answer 62

oh ok

Answer 63

what's another point on this line?

Answer 64

-5?

Answer 65

again, points are locations that must be stated as ordered pairs

Answer 66

look at the attached image

where is the red point located? if you had to give directions, how would you go from (0,0) to that red point?

Answer 67

you can only travel along the grid lines by the way

Answer 68

ok...

Answer 69

start at the origin. How far must you move to the left to get directly underneath the red point?

Answer 70

4 moves to the left..

Answer 71

so the x coordinate of the red point is -4

4 because we moved 4 units
negative because we moved to the left

combine the two to get -4

Answer 72

agreed?

Answer 73

yes

Answer 74

now we're directly underneath the red point. How many units must we move up to get to the red point?

Answer 75

1

Answer 76

so the y coordinate is 1

Answer 77

it's positive because we moved up

Answer 78

x coordinate = -4
y coordinate = 1

the (x,y) location of the red point is (-4,1)

Answer 79

think of it as like an address of where the red point lives

Answer 80

make sense?

Answer 81

yes

Answer 82

so we know the two points (-4,1) and (0,4) lie on this line

Answer 83

what is the slope of the line through (-4,1) and (0,4)

Answer 84

y= -4,0 / 1-4?

Answer 85

what are the y coordinates of the points (-4,1) and (0,4)

Answer 86

1 and 0?

Answer 87

look at the second value of each pairing

Answer 88

1 and 4?

Answer 89

ALL ordered pairs are (x,y)

Answer 90

1 and 4, yes

Answer 91

what is the result if you subtracted?

Answer 92

-3?

Answer 93

1-4 =-3, yes

Answer 94

now subtract the x coordinates in the same order