OpenStudy (anonymous):

HELP! Which is a linear function?

OpenStudy (anonymous):

OpenStudy (john_es):

A linear function is a relation between a variable y and x of the form, \[y=mx+n\]Try to find m and n such that the values of the table verific a relation similar to the this equation.

OpenStudy (anonymous):

I know that you can find the out if it is linear or not by just seeing which was has the same pattern, but I am having trouble with finding out what each of the patterns are.

OpenStudy (anonymous):

I know that A would be out, because the pattern isn't the same each time its different

OpenStudy (john_es):

Ok, and what about C and D, could you say something about them?

OpenStudy (plainntall):

A linear function has a constant slope or constant ration of the change in y over the change in x. Look at each table and see if the slope is constant .

OpenStudy (anonymous):

C doesn't have pattern with the same thing happening, so that would be out too. I do not know if D would, I do not understand how I find out D's pattern

OpenStudy (anonymous):

But I do not think it is D either. I think the answer is B

OpenStudy (plainntall):

The same way for all the choices. The change of x is 1 for each increment, what is the change in y for D?

OpenStudy (john_es):

Perfect. The other, as you said, don't follow the same pattern for each pair (x,y). Could you find the relation for B?

OpenStudy (anonymous):

I don't understand the decimals though. They confuse me

OpenStudy (anonymous):

I am pretty sure it is b, because -2+2=0, and 2+2=4

OpenStudy (john_es):

Yes, it is B, but the relation is, \[y=2x-4\]As you see, \[x=1\Rightarrow y=2-4=-2\\ x=2\Rightarrow y=4-4=0\]And so on. Do you understand it?

OpenStudy (anonymous):

Could anyone help me with this? I do not understand

OpenStudy (plainntall):

Just find the difference between the values 0.5 - 1 = -0.5, 0.33-0.5=-0.27 Since the change of x is 1 for each interval you can already see that the slope is not the same and therefore the function is not linear.

OpenStudy (john_es):

Look the values for f(x). What is their sign?

OpenStudy (anonymous):

What do you mean by sign?

OpenStudy (john_es):

Negative or positive, I mean

OpenStudy (anonymous):

They are positive

OpenStudy (john_es):

Ok, so the function must be in the upper part of the graph. What graphs satisfy this condition?

OpenStudy (anonymous):

c or d?

OpenStudy (john_es):

Very good!

OpenStudy (john_es):

Now, see the table, what value takes f(x) fo x=0?

OpenStudy (anonymous):

3?

OpenStudy (john_es):

Exact, so the function must intercept the y axis in y=3. What graph, between C and D, satisfy this condition?

OpenStudy (anonymous):

Graph D?

OpenStudy (john_es):

Perfect, you solve it ;).

OpenStudy (anonymous):

Great! thank you so much for the help.

OpenStudy (john_es):

Remember the steps for future problems ;)

OpenStudy (anonymous):

I definitely will. Thank you!

OpenStudy (john_es):

You're welcome.