HELP! Which is a linear function?
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.
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.
I know that A would be out, because the pattern isn't the same each time its different
Ok, and what about C and D, could you say something about them?
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 .
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
But I do not think it is D either. I think the answer is B
The same way for all the choices. The change of x is 1 for each increment, what is the change in y for D?
Perfect. The other, as you said, don't follow the same pattern for each pair (x,y). Could you find the relation for B?
I don't understand the decimals though. They confuse me
I am pretty sure it is b, because -2+2=0, and 2+2=4
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?
Could anyone help me with this? I do not understand
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.
Look the values for f(x). What is their sign?
What do you mean by sign?
Negative or positive, I mean
They are positive
Ok, so the function must be in the upper part of the graph. What graphs satisfy this condition?
c or d?
Now, see the table, what value takes f(x) fo x=0?
Exact, so the function must intercept the y axis in y=3. What graph, between C and D, satisfy this condition?
Perfect, you solve it ;).
Great! thank you so much for the help.
Remember the steps for future problems ;)
I definitely will. Thank you!