## anonymous 5 years ago Can someone explain finding the equation of a line step by step

1. 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.

2. anonymous

Okay say im given two points

3. anonymous

Ok, then you must first find the slope.

4. anonymous

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

5. anonymous

No

6. 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.

7. anonymous

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

8. anonymous

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

9. 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.

10. anonymous

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

11. anonymous

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

12. anonymous

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

13. anonymous

Yes, but you can simplify that.

14. anonymous

To 1/2?

15. anonymous

Yes

16. anonymous

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

17. anonymous

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

18. anonymous

Not quite.

19. anonymous

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

20. 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.

21. anonymous

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

22. anonymous

That means you have the slope intercept form.

23. anonymous

y=mx + b

24. anonymous

where the coefficient on the x term is your slope.

25. anonymous

26. anonymous

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

27. anonymous

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

28. anonymous

29. anonymous

30. anonymous

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

31. anonymous

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

32. anonymous

What is m?

33. anonymous

What is b?