Question

What is the equation of the line passing through `(11,17)` and `(23,11)`?

Answer 1

`x+2y=45`

Explanation:

1st point`=(x_1, y_1)=(11, 17)`
2nd point`=(x_2, y_2)=(23, 11)`

First, we will have to find the slope `m` of this line:

`m=(y_2-y_1)/(x_2-x_1)=(11-17)/(23-11)=-6/12=-1/2`

Now, use point-slope formula with one of the given points:
`y-y_1=m(x-x_1)`
`y-17=-1/2(x-11)`
`y-17=-1/2x+11/2`
`y=-1/2x+11/2+17`
`y=(-x+11+34)/2`
`2y=-x+45`
`x+2y=45`

Answer 2

`y = -x/2 + 45/2`

Explanation:

Usung the formula `y-y_1 = m(x-x_1)`
Considering
`(11, 17) and (23, 11)`
`(x_1, y_1) and (x_2, y_2)`

m (gradient) = `(y_2-y_1)/(x_2-x_1)`

m = `(11-17)/(23-11)`

m = `-6/12`

m = `-1/2`

`y-17 = -1/2(x-11)`
`y-17 = -x/2+11/2`
`y = -x/2+11/2+17`
`y = -x/2 + 45/2`

This is the equation of the line