Question

Find an equation for the line passing through the given points. Use function notation to write the answer. (-4,-3) and (-8,-2)...any help would be greatly appreciated!! Thanks!

Answer 1

the function for a line is like the equation of a line, so you hopefully have seen that in the form, y = mx + b where m is the slope and b is the y-intercept.

Answer 2

you can calculate the slope from two points on a line, because slope is the change in the y values divided by the change in the x values... "how far up" compared to "how far over"

Answer 3

so m = (y2 - y1) / (x2 - x1)
= (-3 -(-2)) / (-4 - (-8))
= (-1) / 4
m = -(1/4)

Answer 4

if its y2-y1 wouldn't it be -2+3?

Answer 5

you can do it that direction, that's fine... as long as you choose the same pair as "x2,y2"

So if you choose y2-y1 as -2+3, also choose x2-x1 as -8 - (-4)

Answer 6

you would have 1 on top and (-4) on bottom doing it that way, which is still -(1/4) overall.

Makes sense... the slope of the line doesn't change based on which direction you are looking...

Answer 7

I did -2+4/-8+4 and got 1/2. is that right?

Answer 8

and then y-y1=m(x-x1) so its y+3=1/2(x+4)?

Answer 9

you just made a small mistake... you just told me y2-y1 is -2+3, but above, you showed it as -2 +4 you just made a typo, but it changes the overall slope....

try again, you are on the right track without that typo

Answer 10

i just wrote it wrote. i got -2+4/-8+4.. is that right?

Answer 11

y2 is -2, and y1 is -3

x2 is -8 and x1 is -4

(y2-1y) / (x2-x1) = (-2 + 3) / (-8+4)
= -1 / 4

Answer 12

you just accidentally had y1 as -4.... should be -3

Answer 13

but now that you have slope of -1/4, you can do the point slope form like you did a minute ago.

y-y1=m(x-x1) ----->>>>> y+3 = (-1/4)(x+4)

Answer 14

okay i understand now its 1/-4

Answer 15

okay so with that formula to solve it of you first so distributive property right?

Answer 16

yes, distribute the (-1/4) across the (x+4).

Then, you need to rearrange things to get that +3 off of the left side of the equation... subtract 3 from BOTH sides, so that you have only y on the left. Then simplify the right one more time.

Answer 17

wait, sow hen i distribute -1/4 and 4 is that 1?

Answer 18

-1*

Answer 19

(-1/4)(x+4) = (-1/4)x + (-1/4)(4)
= (-1/4)x + (-1)
= (-1/4)x -1

Answer 20

y + 3 = (-1/4)(x+4)
y + 3 = (-1/4)x - 1
y + 3 - 3 = (-1/4)x - 1 - 3
y = (-1/4)x - 4

Answer 21

Does this make sense?

Step 1: use 2 points to calculate slope by m = (y2-y1)/(x2-x1)
Step 2: use 1 of the points and the slope to express the point-slope form of the line, y-y1 = m(x-x1)
Step 3: simplify the expression by distributing the m across the (x-x1) term, solve for y on the left side of the equation, and simplify the right side to put it all into the form, y=mx+b

Answer 22

okay yes i understand i got the correct answer!

Answer 23

Great, glad to help :)

Answer 24

thank you sooooo much!!!! i really aprecciate it