Question

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

Answer 1

The Equation of (4,3) and (2,2) is y=1/2x+1

Answer 2

The equation of line is
`y=(1)/(2)(x)+1`.

Explanation:

Given information: The line passes through the point (4,3) and (2,2).

If a line passes through the points
`(x_1,y_1)` and
`(x_2,y_2)`, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The line passes through the point (4,3) and (2,2), so the equation of line is

`y-3=(2-3)/(2-4)(x-4)`

`y-3=(-1)/(-2)(x-4)`

`y-3=(1)/(2)(x-4)`

Using distributive property, we get

`y-3=(1)/(2)(x)+(1)/(2)(-4)`

`y-3=(1)/(2)(x)-2`

Add 3 on both sides.

`y=(1)/(2)(x)-2+3`

`y=(1)/(2)(x)+1`

Therefore the equation of line is
`y=(1)/(2)(x)+1`.