Question

Which of the following equations describe the line? pic below

Answer 1

you have two points, determine the slope \[m=\frac{y_2-y_1}{x_2-x_1}\], , ,

Answer 2

that still doesn't help. when there are more than one answer to chose from.

Answer 3

what slope did you get

Answer 4

the point-slope for of a straight line is
\[y – y_1 = m(x – x_1)\]

where the slope is \(m\),
and \((x_1,y_1)\) is one of the points

Answer 5

-7/3=slope i think

Answer 6

*\[y-y_1 = m(x-x_1)\]

Answer 7

hmm not quite
the slope is
\[m=\frac{y_2-y_1}{x_2-x_1}=\frac{8-(-6)}{-1-(-3)}\]

Answer 8

17?

Answer 9

lets look at the numerator first,

8-(-6) = 8+6 = ...

Answer 10

and the denominator

-1-(-3) = -1+3 = . . .

Answer 11

slope is 7

Answer 12

good so you have
\[y-y_1=7(x-x_1)\]
now chose one of the points and sub in its coordinates

Answer 13

try subbing in the point (-3, -6)

Answer 14

[ for (x_1, y_1) ]

Answer 15

in the beginning when trying to find the slope how do i know which is the 1st y and which is the 2nd and for the x's as well?

Answer 16

well i usually choose to index the points form left to right, but you could do it the other way and it should shill give the same result

\[m=\frac{y_2-y_1}{x_2-x_1}=\frac{-(y_2-y_1)}{-(x_2-x_1)}=\frac{y_1-y_2}{x_1-x_2}=\frac{-6-8}{-3-(-1)}=\frac{-14}{-2}=7\]

Answer 17

so it doesn't matter either way?

Answer 18

if you go from right to left there will be minus in the numerator and the denominator and they will cancel

Answer 19

oh okay so after finding the slop plug it in also using one of the points so itd be
y-(-3)=7(x-(-6)?

Answer 20

make sure you get the co-ordinates the right way around


y - y_1 = 7(x - x_1)


(-3 , -6 )
(x_1, y_1)


x_1 = -3, y_1 = -6

Answer 21

ok yea i did it backwards kinda. so itd be y-(-6)=7(x-(-3))

Answer 22

good!

now can you simplify it a bit, by cancelling some negative signs

Answer 23

y+6=7(x+3)

Answer 24

excellent ! so you have found one of the answers

Answer 25

how do i find the other ones?

Answer 26

but what if we had subbed in a different point


y - y_2 = 7(x - x_2)


(-1 , 8 )
(x_2 y_2)


x_2 = -1, y_2 = 8

Answer 27

y-8=7(x+1)

Answer 28

yes,


now notice
that if we rearrange the equation we got for the line using the first point

y+6 = 7(x+3)
y+6 -14 = 7x +21 -14
y - 8 = 7x +7
y - 8 = 7(x+1)


we see that it is equivalent to the equation we got using the second point

Answer 29

where did the -14 come from?

Answer 30

well it looks a bit artificial , but i was just showing one way that we can see the two equations are equivalent

(the -14 made the left hand side what i was aiming for)

Answer 31

if you use -6 (to get y+0=, on the left),

y+6 -6 = 7x +21 -6
y = 7x+15

you get the slope-intercept form of the line, which tells us the line cuts the y-axis at y=15

Answer 32

two of the answers has fractions in them E. y-8=7/2(x+1) and F. y+8=7/2(x-1). how do i figure if those are correct or not?

Answer 33

or would the answers to my question be A. and C.

Answer 34

you got the slope to be 7, which is not a fraction

Answer 35

so unless the slope is a fraction those are not correct and my answers are A. and C.?

Answer 36

correct

Answer 37

okay thank you so much this helped alot :)

Answer 38

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