Question

I did a few of these questions before hand, and now all of a sudden I'm stuck.

I have to find which equation is shown on the graph below and I'm confused because the lines seem to go IN BETWEEN the numbers and I don't know which way to represent it.

See graph below.

Answer 1

The graph shows increase because it goes up left to right so you already know you'll be adding or multiplying

Answer 2

I more inclined to think that I'll be adding.

Answer 3

I would look for points where it's easy to read off an (x,y) point on the line
for example, (0, -4) and (2,0)

Answer 4

the "number labels" are for the "lines", and you know you start at x=0 (for example)
and the "1" goes with the next line over from x=0

Answer 5

Those two pts are clearest.

So you can find the gradient from these pts, then sub one of the pts and this gradient into
y - y1 = m(x - x1) to find the equation.

Alternatively, the two pts are also your x and y intercepts, and the equation of any line with x intercept of A and y intercept of B is given by:

\[\frac{ x }{ A }+\frac{ y }{ B } =1\]

Answer 6

once you have two points, you can find the slope, and then the equation
or you could count: up 4 and over 2 (starting at (0,-4) and going to (2,0) )
that makes the slope (i.e. change in y is up divided by change in x (over) ) 4/2 or 2

Answer 7

Agh! A tad confused with all these variable's of y and slope and points....so I'm just re-reading everything that was written over again.

Answer 8

Okay, so does 2x + y make any sense as an equation for this?
@phi
@mww

Answer 9

I would stick with the formula
y = mx + b

you know m is 2 (that is the slope)
you now need "b", the y-intercept

Answer 10

Well, at the moment I'm stuck with Ax + By = C standard formula.
That is what the whole assignment I'm working on is based off of. Thats specifically what they are trying to teach me.

Answer 11

@Atsie are they asking you to write the equation in general form?

Answer 12

Well, if general form is the way to put it then I suppose so.
y = mx + b has never been mentioned yet.

Answer 13

oh. I guess there might be quick ways to write an equation in standard form, but I would write it in slope intercept form, then translate to standard form.

Answer 14

mww shows how to use the "intercepts" to write the equation in the form
\[ \frac{x}{x-intercept} + \frac{y}{y-intercept} = 1\]
and we can read off the intercepts, so that is easy to write down.

then we "clear the denominators" to make it standard form.
(if that makes sense??)

Answer 15

so, in this special case, where we know both intercepts, we can use the formula
\[ yintercept \cdot x + xintercept \cdot y = xintercept \cdot yintercept \]

Answer 16

you would still want to simplify by factoring out any common multiple.

Answer 17

another way to tackle this is use the idea of ratios, for a line that goes through (0,0)
\[ \frac{y}{x} = m \]
in this case:
\[ \frac{y}{x} = 2 \\ y = 2x\\ 0= 2x - y\\ 2x-y=0\]
then put in a point e.g. (2,0) to get
2*2-0 = 4
to find the right hand side.

you get
2x-y= 4

Answer 18

@phi
Eee! Okay, I'm going to ignore the ratio and intercept thing right now because its absolutely overwhelming and to much information for me to understand.
Do you know of a way though, to do this simply by standard form only? Or have you yourself not really become accustomed to SF ?

Answer 19

Also, I don't have 2x - y = 4 as an option for this question....so I'm extra confused.

Answer 20

I assume that your lesson explains how they want you to do this problem. I'm guessing it's a very specific approach ?

Answer 21

standard form usually means: variables in alphabetical order (so x before y)
and usually, the leading coefficient is make positive.
but you could write it as
-2x+y= -4

Answer 22

can you describe (or post) how they expect you to do this problem ?

Answer 23

Well, I don't know how specifically to describe it but I'll try.
They basically want me doing everything via standard form.
They describe standard form as obviously stated Ax + By = C and then they also say that where \[A \ge 0\] , A and B are not both zero, and A, B, and C are integers with a greatest common factor of 1.
This also ties into the fact that I'm learning about linear equations and functions.

Is that of any help? @phi

I mean basically, they expect me to do it in standard form somehow.

Answer 24

ok, that is what I understand as "standard form"
But, do they give an example of how to translate info on a graph into standard form?

Answer 25

Hmm, let me go look.
Sorry, I should actually have the book open and I'm being a total dunce :P

Answer 26

The only info I'm given really is that the x coordinate of a point at which the graph of an equation crosses the x - axis is called a x-intercept and the y coordinate of the point at which the graph crosses the y axis is called a y intercept.
Then I'm also told that the values of x for something in the case of \[F(x) = 0\] are called zero's of the function f.
So the zero of a function is its x intercept.

Thats all there is.

Answer 27

ok. what grade is this? what course ?

Answer 28

9th grade Algebra I
(don't judge. :P I'm actually supposed to be going into 11th grade math soon but as you can see I'm not great at it)

Answer 29

ok, and do they have an example where they show a graph of a line and explain how to find the equation of the line ?

Answer 30

They literally do not. I've looked all over the place.

Answer 31

can you post a snapshot of the first page of the chapter or section that has this question ?

Answer 32

I am thinking that you learn one way to do this, but I would rather it was in the book.
But *everybody* learns about slope of a line and that is one way to do this problem, so we could learn that.

Answer 33

Alright, here lets go with this.
I am told to read page 173 and thats it.

https://www.mpaper.net/mpaper.php?hash=84a30c61-460c-4394-b11c-c57fdb25a780

Unless there is something else that I'm supposed to read and didn't or unless there is something that I missed...who knows maybe you could find something.

Answer 34

From what I see, they want you to "read off" the x-intercept and the y-intercept
from the graph.
can you do that for this problem ?

Answer 35

Well I can try, but I don't necessarily understand how.

Answer 36

do you know which line is the "x-axis" ? it's the thick horizontal (sideways) line labeled with numbers.

Answer 37

Yes, I do :)

Answer 38

find where the line crosses the x-axis. (mww shows in a post up above)
the "x-intercept" is how far sideways you are on the x-axis away from the "origin"

Answer 39

any idea what the x-value is of the "x-intercept" ?

Answer 40

Its two, isn't it?

Answer 41

yes. and in case it's not obvious, the y-value is 0 (you are not above or below )
so that point has (x,y) numbers of (2,0)

Answer 42

next, what is the "y-intercept" (where the line crosses the vertical y-axis)

Answer 43

Well the y-intercept kind of gets me, because it runs straight into -5 but yet is on -4 at the same time.

Answer 44

ok, but we only care about the "lines"
the labels are there for convenience (otherwise you would have to count, starting from the origin)

Answer 45

For example