Math Homework?

Question

I have a fuction table.x y
-4 7
-5 4
-6 1
What is the rule?

The function

A simple rule BTW.I.E.-y=x=5-19

Answer 1

Easy as pie!
You can see that the X (or IN) side is going DOWN by 1 each line...(-4 -1 = -5, -5-1 = -6)

We can see that the Y (or OUT) side is going DOWN by 3 each line...(7-3=4, 4-3=1)

So, for each step DOWN on the IN side, you go DOWN by 3 - or, to put it the other way, for each step UP the IN side, you go UP by 3 on the OUT side.

You can find the equation for the line that this represents too...

We know the general equation of a line is Y=MX+B where M is the slope (rise/run) and B is the Y-Intercept (Where X is 0).

Here we see that our slope is: (1-4)/(-6 - -5) or (-3/-1) or 3
So...Y=3X+B
Let's clock our way UP to 0 by applying our RULE...
-3 10
-2 13
-1 16
0 19
...So we can see the Y-Intercept is 19...
Y=3X+19

Does it work? Let's test it!

Let's plug in -5 for X and see...
3 *(-5) + 19
-15+19=4
And that matches what we expect to see, so we've got it!

Hope this helps.

Orion

Answer 2

You just need to know a simple formula.
Y-y^1=m(X-x^1).........................(m=slope)

First find the slope, y-y over x-x. (the slope here is 3)

Now pick any ordered pair from the table. Plug Y(from the ordered pair) in for y^1, and the X in for x^1 into the formula. Any ordered pair will do. It will work the same each time guaranteed!

If you did it the way I did, the answer would be...

y-4=3(x+5).........simplify....
y-4=3x+15...............get y alone....
y=3x+19........................................
now go back to the table, and pick an x. I chose the ordered pair(-6, 1)
Put the x in so you get
Y=3*-6+19
3*-6= -18
so, y=-18 +19....or y=1

The rule is y=3x+19

Answer 3

as x goes down by 1, y goes down by 3