Question

What is the equation of the line that goes through `A( 1,- 5)` and `B ( 7,3)`?

Answer 1

`4x-3y=19`

Explanation:

After using line equation which goes through 2 points,

`(y-3)/(x-7)=(3-(-5))/(7-1)`

`(y-3)/(x-7)=8/6`

`(y-3)/(x-7)=4/3`

`3*(y-3)=4*(x-7)`

`3y-9=4x-28`

`4x-3y=19`

Answer 2

`y =( 4x)/3 -19/3` or could be re-written as `3y = 4x -19`

Explanation:

The general formula for a straight line is
`y = mx + c` where `m` is the slope and `c` is the `y` intercept (the point at which the line crosses the y axis#

Given two points the slope can be calculated as
`m=(y_2-y_1)/(x_2-x_1)`

Substitute in what we know
`m = (3--5)/(7-1) = 8/6 = 4/3`

so now we have
`y =( 4x)/3 +c`

To calculate c, substitute `x` and `y` for one of the points given
`3 =4*7/3 + c`

Multiply throughout by 3
`9 = 28 + 3c`

And simplify
`-19 = 3c`

`c = -19/3`

our equation now looks like
`y =( 4x)/3 -19/3` or could be re-written as `3y = 4x -19`