Math function rule question

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- bealiberty47

Math function rule question

- schrodinger

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- bealiberty47

##### 1 Attachment

- mathstudent55

First, look at the points you are given.
Do they seem to be linear or not? To see if they are linear, see if the same change in x has the same change in y.

- mathstudent55

If they are linear, then choose two points and find the equation of the line through them.

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## More answers

- bealiberty47

There isn't a same change because while Y goes up x2, X goes down randomly

- bealiberty47

So it's not linear?

- bealiberty47

can you help me @geerky42

- bealiberty47

- mathstudent55

No.
Don't compare with multiplication.
Compare with subtraction.

- Pawanyadav

Try to plot its graph it clarify everything to you

- mathstudent55

Here are the points:
x 2 4 6
y 1 0 -1

- mathstudent55

I will write the differences between each x-coordinate and the previous one on the line above the x-coordinates. I will do the same for the y-coordinates below the y-coordinates
2 2
x 2 4 6
y 1 0 -1
-1 -1

- mathstudent55

Notice that as x goes from 2 to 4, the difference is 2.
As x goes from 4 to 6, the difference is again 2.
Now look at y.
As x goes from 2 to 4, y goes down by 1.
As x goes from 4 to 6, y again goes down by 1.
Every time x increases 2, y decreases 1.
That is a linear relation.

- bealiberty47

x + 2 = y - 1

- mathstudent55

Now that you see it's a linear relation, pick any two points.
Then find the slope of the line between the two points.
Do you know how to find the slope of a line given two points on the line?

- bealiberty47

no please explain

- mathstudent55

For points \((x_1, y_1)\) and \((x_2, y_2) \), the slope opf the line through those points is:
\(slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} \)
In other words, subtract the y-coordinates. Subtract the x-coordinates.. Divide the first difference by the second difference.

- mathstudent55

That gives you slope.
Then we have a little more work to find the equation.

- bealiberty47

just give me a minute

- bealiberty47

4,0 - 2,1 = -1/2?

- bealiberty47

or is it 2,1 - 4,0 = 1/2

- bealiberty47

- mathstudent55

If you use the points (4, 0) and (2, 1), you get:
\(m = \dfrac{0 - 1}{4 - 2} = \dfrac{-1}{2} = -\dfrac{1}{2} \)

- mathstudent55

The slope is -1/2
Now we need to get the equation of the line.
The slope-intercept form of the equation of t a line is
\(y = mx + b\), where m = slope and b = y-intercept.
We know the slope is -1/2. We need to find b.
We use one of our 3 points in the equation and solve for b.
\(\color{red}{y} = \color{green}{m}\color{blue}{x} + \color{brown}{b}\)
Let's use point \((\color{blue}{4}, \color{red}{0})\). We replace \(\color{blue}{x}\) with \(\color{blue}{4} \) and \(\color{red}{y} \) with \(\color{red}{0}\). We replace \(\color{green}{m}\) with \(\color{green}{-\dfrac{1}{2}}\), since \(\color{green}{m}\) is the \(\color{green}{slope}\) and the \(\color{green}{slope}\) is \(\color{green}{- \dfrac{1}{2}} \).
\(\color{red}{0} = \color{green}{-\dfrac{1}{2}} (\color{blue}{4}) + \color{brown}{b}\)
\(0 = -2 + b\)
\(b = 2\)
Now that we know b = 2, we can write the equation of the line:
\(y = -\dfrac{1}{2}x + 2\)

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