Can someone explain finding the equation of a line step by step

- anonymous

Can someone explain finding the equation of a line step by step

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- anonymous

There are a number of ways to do it depending on what information you have. Typically you'll be given either a point and a slope, or given 2 points.

- anonymous

Okay say im given two points

- anonymous

Ok, then you must first find the slope.

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- anonymous

Do you know how to find the slope of a line, given 2 points?

- anonymous

No

- anonymous

\[Slope =\frac{y_2-y_1}{x_2-x_1}\]
Where \((x_1,y_1)\) is the first point and \((x_2,y_2)\) is the second.

- anonymous

The slope is how much the function (y) changes as the input (x) changes.

- anonymous

Our teacher said it's pretty much rise over run correct?

- anonymous

So
\[ Slope = \frac{\text{Change in y}}{\text{Change in x}}\]
And we can find the difference in x and the difference in y by subtracting the x and y values at the respective points.

- anonymous

Yes. How much you rise over how far you ran.

- anonymous

Once you know the slope, you can plug in the slope, and one of your points into the point slope formula.

- anonymous

So if I had a line that passes through (2,4) and (8, 7) wouldn't the slope be 3/6

- anonymous

Yes, but you can simplify that.

- anonymous

To 1/2?

- anonymous

Yes

- anonymous

Now plug that slope into the point slope formula along with one of your points.

- anonymous

Okay so if I had (-4,8) and (3, 1) It would be 7/7?

- anonymous

Not quite.

- anonymous

Double check that you are putting the same point for x1 that you're putting for y1 and vice versa.

- anonymous

It doesn't matter which one you pick to be point 1 or point 2, but you have to keep them consistant. You can't use one for point 1 on top, then switch it on the bottom.

- anonymous

Okay, makes sense. So say they give me just y=-2x, what does that mean

- anonymous

That means you have the slope intercept form.

- anonymous

y=mx + b

- anonymous

where the coefficient on the x term is your slope.

- anonymous

m is your slope.

- anonymous

So how do I put it into y=mx+b form?

- anonymous

b (the constant term) is the y value where the line crosses the y axis.

- anonymous

It is in y=mx+b already

- anonymous

What is your m?

- anonymous

Well Im not sure, the problem is matching up the graphs to the equation
'

- anonymous

No, I'm saying if you have an equation
y = -2x
y = -2x + 0
y = mx + b
It is in slope intercept form.

- anonymous

What is m?

- anonymous

What is b?

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