Question

Determine the equation of the line, in slope-intercept form, that will get your spacecraft from Point B to Point C.
Point B: (3,5)
Point C: (5,3)

Answer 1

I know it's y=mx+b I just need help plugging the numbers in

Answer 2

would it be 5=1/2+ whatever b is...not sure?

Answer 3

Use this :
m=Y2-Y1/X2-X1
X1=3
Y1=5
We just want (-2,3) Caz formula is this :
Y2-Y=m(X2-X)
X2=5
Y2=3

Answer 4

But I thought slope intercept form way y=mx+b?

Answer 5

*wass

Answer 6

It is...and you can use it to find the values of \(m\) and \(b\)

Answer 7

So m is not 1/2 in this one?

Answer 8

Let's see...plug in the points:

3 = 5m + b
5 = 3m + b

b = b

3 - 5m = 5 - 3m
3 - 5 = 5m - 3m
-2 = 2m
-2/2 = m
-1 = m

Looks like the slope is m = -1

Answer 9

oh okay so would y be 5, like 5=-1+ then what ever b is?

Answer 10

Basically, there is a specific set sequence of steps to use to write the equation of a line in point-slope form. But, in short, all you need to do is find the values of \(m\) and \(b\) then plug them in to the original formula.

Answer 11

We found \(m\) but we need to find \(b\).

Answer 12

In order to find \(b\) we will use the value of the slope along with one of the given points and insert them into the formula. Let's just use (3,5):

\(y = mx + b\)
\(3 = -1(5) + b\)

Answer 13

so Would it be like 3=5b?

Answer 14

You are changing the equation

Answer 15

It's 3 = -5 + b

Answer 16

You can't just get rid of the plus

Answer 17

And you can't multiply 5 with b

Answer 18

So how do I get b If I can't do anything to it?

Answer 19

You have to get b by itself. It's called "isolating"

Answer 20

To get b by itself, you have to add 5 to both sides:

3 = -1(5) + b
3 = -5 + b
5 + 3 = b
8 = b

Answer 21

Oh duh...I feel smart :).. so In the equation would it be 5=-1+8?

Answer 22

or would 3 be y?

Answer 23

The equation of a line has to be in the form y = mx + b

Answer 24

You don't get rid of any of the variables, however, you can replace m and b with their equivalent values.

Answer 25

Remember, that's what I was telling you all along. That we will find the values of \(m\) and \(b)\) then insert those values in to the formula.

Answer 26

\(y = \color\red{m}x + \color\red{b}\)

Answer 27

The variables \(m\) and \(b\) are replace with the values we found for them.

Answer 28

okay so y=-1x+8

Answer 29

Yes, finally...

Answer 30

YEAH! Thank you so much... You've been so helpful, I suck at math lol :)