Question

A line passes through 2, -1 and 4, 5 what is the equation

Answer 1

y1 - y2 / x1 - x2

-1 - 5 / 2 - 4

-6/-2

3

y = mx + b

-1 = 3(2) + b

-1 = 6 + b

-7 = b

y = 3x - 7

Hope this helps! ;)

Answer 2

The equation is
`3x -y =7`

Solution:

Let us assume that the
`(x_1, y_1) = (4,5)` and
`(x_2, y_2) = (2,-1)`

The slope of the line m is
`=(y_2-y_1)/(x_2-x_1)=(-1-5)/(2-4)=\left((6)/(2)\right)=3`

We know the equation of a line at a given point
`(x_1,y_1) is (y-y_1) = m(x-x_1)`

Let me take the point (4,5) here,

So the equation of the line is

`(y-5)=3 *(x-4)`

`y-5=3 x-12`

`3x-12 - y+5 = 0`

`3x -y -7 =0`

`3x -y =7`

So, the equation is
`3x-y =7`