Question

HELP! Which is a linear function?

Answer 1

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.

Answer 2

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.

Answer 3

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

Answer 4

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

Answer 5

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 .

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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?

Answer 13

Could anyone help me with this? I do not understand

Answer 14

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.

Answer 15

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

Answer 16

What do you mean by sign?

Answer 17

Negative or positive, I mean

Answer 18

They are positive

Answer 19

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

Answer 20

c or d?

Answer 21

Very good!

Answer 22

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

Answer 23

3?

Answer 24

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

Answer 25

Graph D?

Answer 26

Perfect, you solve it ;).

Answer 27

Great! thank you so much for the help.

Answer 28

Remember the steps for future problems ;)

Answer 29

I definitely will. Thank you!

Answer 30

You're welcome.