Question

Find the equation of the line going through the points (2,-1) and (5,2) 3x 2y

Answer 1

The equation of the line is:

`y = x - 3`

Explanation:

The general equation of a straight line is given by:

`y = ax + b`

Being given two points, we can replace x and y, solve the system and find the values for a and b.

Solution:

The line goes through the point
`(2,-1)`. It means that when
`x = 2, y = -1`. Replacing in the equation:

`y = ax + b`

`-1 = 2a + b`

`2a + b = -1`

The line also goes through the point
`(5,2)`. It means that when
`x = 5 y = 2`. Replacing in the equation:

`y = ax + b`

`2 = 5a + b`

`5a + b = 2`

Now we have to solve the following system of equations:

`1) 2a + b = -1`

`2) 5a + b = 2`

From 1), we have:

`b = -1 - 2a`

Replacing in 2)

`5a - 1 - 2a = 2`

`3a = 3`

`a = (3)/(3)`

`a = 1`

`b = -1 - 2a = -1 - 2 = -3`

The equation of the line is:

`y = x - 3`