Question

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

Answer 1

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.

Answer 2

Okay say im given two points

Answer 3

Ok, then you must first find the slope.

Answer 4

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

Answer 5

No

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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.

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

Yes, but you can simplify that.

Answer 14

To 1/2?

Answer 15

Yes

Answer 16

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

Answer 17

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

Answer 18

Not quite.

Answer 19

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

Answer 20

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.

Answer 21

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

Answer 22

That means you have the slope intercept form.

Answer 23

y=mx + b

Answer 24

where the coefficient on the x term is your slope.

Answer 25

m is your slope.

Answer 26

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

Answer 27

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

Answer 28

It is in y=mx+b already

Answer 29

What is your m?

Answer 30

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

Answer 31

No, I'm saying if you have an equation

y = -2x
y = -2x + 0
y = mx + b
It is in slope intercept form.

Answer 32

What is m?

Answer 33

What is b?