Hi resident math pros.

My son has math homework and I swear I'm going to lose my mind.

Unky, Morgaine, someone, please help me understand how to do this so I can help him.

I really don't remember doing this in school.

I'll try to explain this as best I can, and if I'm not understanding this right, please tell me. :)

It's an Input/Output machine.

Two columns, side by side, one Input, the other Output.

Each column has numbers.

From what I understand you have to figure out the equation that works for all the columns. These are the actual instructions, in case I'm reading this wrong (could be, it's been a long day)

Here is an input/output machine that uses two operations.

Here is a table for the machine (the table is the columns with those numbers I posted)

Find out what the machine does to each input number.

So, in the input column we have 2, 4, 6, 8 (obviously going up by 2's)
The output column has 7, 15, 23, 31 (going up by 8's)

How the heck do you get the equation?

It would be 2 (the equation) = 7
4 (the equation) = 15
6 (the equation) = 23
8 (the equation) = 31

Can someone walk me through grade 6 math please? Pretty please?

It looks like the equation is 4n - 1 where n is the input number.
As we used to say (inn the pre-electric olden times) "plug it in and turn the crank."
Plug in 2, turn the crank [ 4 x 2 = 8 -1 = 7]
Plug in 4, turn the crank [4 x 4 = 16 - 1 = 15]
Etc.

Hi Alty,

I think what they have here is the need to find one equation that will generate the output numbers given when the input number are inserted. What I see is that is each case if the input number is multiplied by 4 and then 1 is subtracted, you get the output number. For example:

(2 x 4) -1 = 7

(4 x 4) -1 = 15

and so on

x 4 - 1 just from looking at it
Let's see... going up by +8 is 4 times going up by +2, but at the start of the list the 7 is 1 off from 2 x 4, so all subsequent numbers will be too.
Is that how 6th graders have to say it?

Wow!

Thanks guys.

I feel a bit foolish now.

Thanks so much. :)

Well, I think that J is starting his course in functions. As such, I guess that he knows by now that a one-one function is one where there is only one 'output' to a certain 'input'

The input will be x and the output f(x).

As you have noted, there is only one corresponding value in the output for a particular input, the function is a one one function. Another thing you correctly noted is that they go up by the same amount each time, and this suggests a linear function.

Since it is linear, you can imagine the points to make a straight line on graph paper, if you plot (2,7), (4,15), (6,23), (8,31).

Hence, you can find the gradient of the line (or slope).

Take any two coordinates, subtract the outputs and the inputs like this:

\frac{15-7}{4-2} = \frac82 = 4

So, your line has a gradient (or slope) of 4.

To now find the equation, do again the same thing, but with y and x, like this, and equate to the gradient:

\frac{y-7}{x-2} = 4

J should be able to cross multiply, and simplify:

y-7 = 4(x-2)

y-7 = 4x - 8

y = 4x - 8 + 7

y = 4x-1

And you now replace y by f(x) (it's a matter of presentation because this is a function)

f(x) = 4x - 1

~~~~~~~~~
Maybe the gradient part is not so clear, so, here's another example:

If you have (x_1, y_1)\ and\ (x_2, y_2)

The gradient is given by:

\frac{y_2-y_1}{x_2-x_1}

The equation of the line:

\frac{y-y_1}{x-x_1} = m

where m is the gradient of the line.

I hope you understand :)

If you need clarification, just ask :)

Thanks everyone. What would I do without all of you?

Stick around because Jared still has 6 years of school to go, unless he goes to college in which case he's on his own. ;)