Question

Please help 3 questions!
1. Which is an equation of the line that contains the points (0,3) and (-2,4)
A. 2x + y = 3
B. x + 2y = 6
C. 2x + y = 0
D. x - 2y = 6
2. A line contains the point (-3,-1) and has a slope of 1/3. which equation represents this line?
A. x + 3y = 0
B. x - 3y = 0
C. 3x + y = 0
D. 3x - y = 0
3. Which is an equation of the line that contains the points (0,2) and (4,0)?
A. x + 2y = 4
B. x - 2y = 4
C. 2x + y = 4
D. 2x - y = 4

Answer 1

1.) get the slope of the line..
\[m = \frac{ 4-3 }{ -2-0 }\]
you're given with the y-intercept as (0,3) so plug it all in to
y = mx+b
where m is the slope and b is the y-intercept

Answer 2

Ok

Answer 3

so it would be -1/2?

Answer 4

yep now you have m=-1/2 and b=3
so substitute

Answer 5

y=-1/2x+3?

Answer 6

How do i substitute it?

Answer 7

i put?

Answer 8

\[y = mx + b\]
\[y = -\frac{ 1 }{ 2 }x + 3\]
find the LCD for the terms at the right
\[y = \frac{ (-1)x+2(3) }{ 2 }\]
cross multiplt 2 to the left
\[2y = -x + 6\]
now rearrange by transposing -x to the left

Answer 9

do you subtract 6 from both sides?

Answer 10

oh wait

Answer 11

nope
just add x to both sides so that the right side will be left with the constant

Answer 12

x+2y=6?

Answer 13

yep

Answer 14

oh

Answer 15

2. since you have a point(-3,-1) and a slope=1/3
just use the slope equation
\[m = \frac{ y-y _{1} }{ x-x _{1} }\]
where m=1/3 and (x1,y1) is (-3,-1)
just substitute

Answer 16

so it would be m = 1/3 ?/-3,-1

Answer 17

yep
\[m = \frac{ y-y _{1} }{ x-x _{1} }\]
\[\frac{ 1 }{ 3 } = \frac{ y-(-1) }{ x-(-3) }\]

Answer 18

Oh

Answer 19

simplify that

Answer 20

remember that when dealing with these problems,
it will just revolve around 2 formulas/equations:
Slope-intercept form:
\[y=mx+b\]
and
Slope formula
\[m = \frac{ y-y _{1} }{ x-x _{1} }\]

Answer 21

what did you get?

Answer 22

I don't know how to do O_O

Answer 23

1/3 = -1y/-3x?

Answer 24

\[\frac{ 1 }{ 3 } = \frac{ y-(-1) }{ x-(-3) }\]
\[\frac{ 1 }{ 3 } = \frac{ y+1 }{ x+3 }\]
cross multiply
\[1(x+3) = 3(y+1)\]
distribute 1 and 3 to respective quantities
\[1(x)+1(3) = 3(y) +3(1)\]
\[x+3 = 3y + 3\]
subtract both side with (x+3)
\[x+3-x-3 = 3y + 3 - x -3\]
\[0 = 3y -x\]
\[3y-x=0\]

Answer 25

So B?

Answer 26

yep

Answer 27

3. you're given with y-intercept as (0,2) so m=2
just find the slope using the slope formula

Answer 28

so use m = y1-y2/x1-x2?

Answer 29

or y=mx+b?

Answer 30

the first one m=...

Answer 31

ok

Answer 32

use the given points (0,2) and (4,0)

Answer 33

so it would be m = 2-0/0-4?

Answer 34

yep

Answer 35

which would be m = 2/-4?

Answer 36

yep or reducing it to lowest form
m = -1/2

Answer 37

now you are ready to substitute to the equation
y=mx+b

Answer 38

m = -1/2, b = 2

Answer 39

ok so y = 1/2x + 2

Answer 40

\[y = -\frac{ 1 }{ 2 }x + 2\]
getting the LCD
\[y = \frac{ -1(x) +2(2) }{ 2 }\]
cross multiply
\[2y = -x + 4\]
add x to both right and left

Answer 41

Uh so x - 2y = 4?

Answer 42

it would cancel it out and it would be 2x = 4?

Answer 43

2y +x = -x + 4 +x

Answer 44

2y + x = 4

Answer 45

oh so A?

Answer 46

Thank you for helping me

Answer 47

yep

Answer 48

I give you medal and fan you

Answer 49

yw :) just keep on practicing for it to retain on your memory

Answer 50

OK ty