Question

What is the equation of the line that passes through (4, -1) and (-2, 3)?

Answer 1

First of all, remember what the equation of a line is:

y = mx+b

Answer 2

right

Answer 3

m=slope
b=y intercept

Answer 4

yea

Answer 5

rise over run = 2/2?

Answer 6

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
\[m=y2 - y1 / x2 - x1 \]

Once you plug in the information, the slope you should get is -2/3

Answer 7

(3-(-1))/(-2-4)

Answer 8

Now let's find the yintercept!

Answer 9

ok!

Answer 10

The b is what we want. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (4,-1) and (-2,3).

Answer 11

Plug in for x and y from one of our (x,y) points that we know the line passes through.

Answer 12

This will allow us to solve for b for the particular line that passes through the two points you gave! You can use either (x,y) point you want..the answer will be the same:

(4, -1). y=mx+b or -1=-2/3 *4+b
or solving for b:
b=-1-(2/3)(4)
b=5/3

Answer 13

OR

Answer 14

(-2,3). y=mx+b or 3=-2/3*2+b
or solving for b:
b=3 -(-2/3)(-2)
b=5/3

Same answer!

Answer 15

This is what will complete our problem.

Answer 16

The final answer will be:

y=-2/3x+5/3

Answer 17

Ok im sorta understanding it.

Answer 18

=) Hope this helped!

Answer 19

Good. Just keep practicing. You'll get it!

Answer 20

Wait how would that look in general form because the awnser to my problem is compley different

Answer 21

Answers*

Answer 22

The "General Form" of the equation of a straight line is:

Ax + By + C = 0

Answer 23

Is that what they look like on your answers?

Answer 24

Step 1: Calculate the slope (m) from the coordinates: (y2 - y1) / (x2 - x1)
and reduce the resulting fraction to the simplest form.

Step 2: From the slope, calculate variables A and B with the equation:
Slope = - A / B

Step 3: Calculate the variable C by applying one of the coordinates to
the equation: Ax + By = -C

Result: Now you have calculated all three variables (A, B and C) for the
General Form Linear Formula.

For your example:

-2x - 3y +5 =0

Answer 25

Good luck!

Answer 26

=)