Question

Find the slope of the line on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.

Graph is in the comments.

@NobodyOwens @agent0smith

Answer 1

@e.mccormick

Answer 2

Slope is change in y over change in x. So pick two points the line goes through, then see how much things change.

Answer 3

What points do I pick?

Answer 4

Any two, but generally I would choose two that are next to each other. I see 5 points where the line crosses at easy to know points.

Answer 5

2 and 1?

Answer 6

Or wait 1 and 1

Answer 7

See, here are the 5 points. At each point I drew an green arrow for the change in y and a yellow one for change in x. See how all of the green arrows are the same length and all the yellow arrows are the same length? So you use the length and direction of one green arrow as the y. Then you use the length and direction of one yellow arrow as the x.

Answer 8

So the points are, (-6,5), (-3,3), (0,1), (3,-1), and (6,-3). Any two of those would get me the slope.

Answer 9

Slope \(m=\dfrac{\Delta y}{\Delta x}=\dfrac{y_2-y_1}{x_2-x_1}\) where \((x_1,y_1)\) and \((x_2,y_2)\) are ANY two points on the line.

Because they are any two points, you can also start at one point, make an arrow, count how many lines it crosses, make another arrow, count how many lines it crosses, not their direction, and use that. That method is what my modified picture is about.

Answer 10

Uhm.. O_o so confused lol.. I suck at Algebra ugh.. I hate it =/.

Answer 11

Well, pick two of the points I listed. Any two.

Answer 12

(0,1)

Answer 13

Use one point, does not matter which, as the \((x_1,y_1)\) values. Then use some other point, any other one, as the \((x_2,y_2)\) values. Then put them in that formula I listed:

\(\dfrac{y_2-y_1}{x_2-x_1}\)

It will give you the slope.

In fact, you could try this a few times with different points and see that they all give you the same slope.

Answer 14

I don't know how to do that.. Is that to the second exponent and the first exponent?

Answer 15

No, those are subscripts. They just help when there is more than one x or y value.

You saw the list of points. Pick two. Any two.

Answer 16

(0,1)

Answer 17

Ok, so that is the first one. What is the second?

Answer 18

(3,-1)

Answer 19

OK, if those are your two points, then you can do this:

\((x_1,y_1)=(0,1)\) and \((x_2,y_2)=(3,-1)\)

Can you see how you need to put the numbers from there into the formula?

Answer 20

\[\LARGE \frac{ -2 }{ 3 }\]

Is this correct? @e.mccormick

Answer 21

Yah, but the - can be moved out front.
\(\dfrac{-2}{3}=-\dfrac{2}{3}=\dfrac{2}{-3}\)

Any of the three will mean the same thing.

Answer 22

Okay so is that the final answer for the slope? =]

Answer 23

Yep! That is all there is to it!

Answer 24

Thanks so much bro! You're a life saver! You're a huge help just.. Can't thank you enough! =]!!!

Answer 25

np. Hope you got how to do it!