anonymous
  • anonymous
Can someone explain finding the equation of a line step by step
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • 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
  • anonymous
Okay say im given two points
anonymous
  • anonymous
Ok, then you must first find the slope.

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anonymous
  • anonymous
Do you know how to find the slope of a line, given 2 points?
anonymous
  • anonymous
No
anonymous
  • 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
  • anonymous
The slope is how much the function (y) changes as the input (x) changes.
anonymous
  • anonymous
Our teacher said it's pretty much rise over run correct?
anonymous
  • 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
  • anonymous
Yes. How much you rise over how far you ran.
anonymous
  • anonymous
Once you know the slope, you can plug in the slope, and one of your points into the point slope formula.
anonymous
  • anonymous
So if I had a line that passes through (2,4) and (8, 7) wouldn't the slope be 3/6
anonymous
  • anonymous
Yes, but you can simplify that.
anonymous
  • anonymous
To 1/2?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
Now plug that slope into the point slope formula along with one of your points.
anonymous
  • anonymous
Okay so if I had (-4,8) and (3, 1) It would be 7/7?
anonymous
  • anonymous
Not quite.
anonymous
  • anonymous
Double check that you are putting the same point for x1 that you're putting for y1 and vice versa.
anonymous
  • 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
  • anonymous
Okay, makes sense. So say they give me just y=-2x, what does that mean
anonymous
  • anonymous
That means you have the slope intercept form.
anonymous
  • anonymous
y=mx + b
anonymous
  • anonymous
where the coefficient on the x term is your slope.
anonymous
  • anonymous
m is your slope.
anonymous
  • anonymous
So how do I put it into y=mx+b form?
anonymous
  • anonymous
b (the constant term) is the y value where the line crosses the y axis.
anonymous
  • anonymous
It is in y=mx+b already
anonymous
  • anonymous
What is your m?
anonymous
  • anonymous
Well Im not sure, the problem is matching up the graphs to the equation '
anonymous
  • 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
  • anonymous
What is m?
anonymous
  • anonymous
What is b?

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