Question

How do you find the equation of line L that passes through the points (1,3) and (-3,4)?

Answer 1

The answer is: `y=-1/4x+13/4`.

It is possible to use this formula, that is the formula to find a line given two points `A(x_A,y_A)` and `B(x_B,y_B)`:

`(y-y_A)/(y_B-y_A)=(x-x_A)/(x_B-x_A)`.

So:

`(y-3)/(4-3)=(x-1)/(-3-1)rArry-3=-1/4(x-1)rArr`

`y=-1/4x+1/4+3rArry=-1/4x+13/4`.

Answer 2

I created a video that answers the question and shows you how to check you work.
http://www.frontporchmath.com/topic/equation-of-a-line-question-1/

To solve this problem you first find the slope of the line, using the two points `(1,3)` and `(-3,4)`.

`(Delta y)/(Delta x) = (4 - 3)/(-3 - 1) = -1/4`

Then you use the y-intercept equation of a line using the slope above and one of the above sets of points to find the y-intercept.

`y = mx + b`
`4 = -1/4(-3) + b`
`4 = 3/4 + b`
`3 1/4 = b`

Then just plug that information into `y=mx+b`

`y= -1/4x +3 1/4`
or
`y=1/4x +(13)/4`