Question

write the slope intercept form of the equation of the line through the given points
through: (3,2) and (2,5)

Answer 1

Start by calculating the slope, which is "m":\[m = \frac{ y _{1} - y _{2} }{ x _{1} - x _{2} }\]where you use your given points which are in the form:\[(x _{1}, y _{1})\]and\[(x _{2}, y _{2})\]

Answer 2

okay dont leave yet

Answer 3

Once you have your "m", you then use the point-slope form of the equation for a line:\[y - y _{1} = m(x - x _{1})\]where you can use either point for the substitution here.

The third step is to rearrange the point-slope form of the equation into the slope-intercept form.

Another way to do this is to graph, but algebra is the way to go, really.

Answer 4

okay so
5-2 over 2-3 equals 3/-1 which is equal to -3

so my slope is -3

Answer 5

Yes, you're doing good so far. You can now go to step 2.

Answer 6

okay hold on

Answer 7

what do you mean by y-y1? like i know what y1 is but whats y?

Answer 8

That's actually a very very good question. And there is a very very good answer which I can give you. It's good you ask because it shows you are thinking well instead of just following a recipe.

y1 and x1 and y2 and x2 are specific values for x and y. In your mind you have to accommodate them as specific and "constant". We have specific values for them given in the problem. But sometimes we are not given specific values for them, but they still remain as SPECIFIC values and constants (they in that case would just not have a given numerical equivalent).

"x" and "y" without the subscripts are true variables and can range over a multitude of values.

Answer 9

so then it would be: y-2=-3(x-3)?

Answer 10

You have just now completed the second step and are doing quite well! Very commendable! Do you want to attempt the third step or do you need help with that? The third step is getting it into the slope-intercept form.

Answer 11

That form is y = mx + b

Answer 12

thank you. so for the slope intercept form, can you kinda walk me through that with the equations that i now have?

Answer 13

should i distribute the -3(x-3)?

Answer 14

Yes, you should distribute. I was starting to finsih the equation, but if you want to attempt it, that is actually much better for your learning.

Answer 15

okay hold on

Answer 16

y-2=-3x+9

Answer 17

should i add 2 to both sides?

Answer 18

Yes, you are understnading this really well. I wish all the people I tutor here could catch on as well as you are doing.

Answer 19

i usually suck at math... so im just lucky tonigt i guess

Answer 20

y=-3x+11

Answer 21

would that be the correct answer?

Answer 22

Well, you are certainly doing well here. Success in Math has a lot to do with attitude, positive attitude that is. Also concentration, patience, and memory play a big role. So does imagination and retention. Math is a vertical area of study. You can't go to the next steps without mastering the basics. Some people stall at those steps and develop "math anxiety" and a bad outlook. But it can be quite fun if you take it one step at a time.

And yes, you got the right answer! Good job!

So that you consolidate your understanding, when you have time, you might want to give this whole thread a once-over. That always helps a LOT!

Answer 23

okay thank you so so much. i have another one here on my worksheet, it is passing through: (4, -2) and (2,4) so do you mind if i solve it real fast then double check with you that i did the correct processs?

Answer 24

itll take me a few minutes

Answer 25

Sure that's fine.

Answer 26

okay thanks.

Answer 27

is the correct answer y=-3x+14?

Answer 28

You got the slope fine, but you made an erro either when putting it into the point-slope form (step #2) or into the slope-intercept form (step #3). It was probably at step #3 and you probably just went fast with your algebra. You understand the concepts well. You just need to concentrate a little more and slow down a little. The answer is :

y = -3x + 10

Answer 29

okay hold on, lemme check my work

Answer 30

howd you get the 10? i keep getting 14 as my y intercept

Answer 31

once i distribute i get y-2=-3x+12, then i add 2 to both sides

Answer 32

np, I'll show you my steps, starting from step #2, because you apparently have no problem getting the slope.

y - (-2) = -3(x - 4) -> y + 2 = -3x + 12

y = -3x + 10

I see where you went wrong. You did y - 2 instead of y - (-2)

Answer 33

okay, yeah i was kinda confused there. im glad you were able to see where i went wrong. when i went back, i did end up getting y=-3x+10

Answer 34

And it is no problem making mistakes. Mistakes are completely fine as long as you can learn from them. You did really, really well and I'm especially glad that you don't let a small mistake get you down. You really are doing fine. Just keep up the good work and review this whole thing. Absolutely wonderful working with you!

Answer 35

you too thanks

Answer 36

Hope to see you in the future but for now I have to go. Good luck in all your studies!

Answer 37

thanks, i aprreciate your help