Question

A line passes through the points (4,6) and (6,2)

Select Yes or No to tell whether each equation describes this line.
(image attached)

Answer 1

Option 2 and option 6 are correct which is
`(y-6)=-2(x-4)` and
`(y-2)=-2(x-6)` respectively.

Step-by-step explanation:

We have been given two points (4,6) and (6,2)

We have formula for equation of a line which is

`(y-y_1)=m(x-x_1)`

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

Here,
`{x_1=4,y_1=6,x_2=6,y_2=2`

On substituting the values we will get
`m=(2-6)/(6-4)=-2`

Now, substituting values in
`(y-y_1)=m(x-x_1)` we will get

`(y-6)=-2(x-4)`

If we choose
`x_1=6,y_1=2,x_2=4,y_2=6` then substituting the values in
`(y-y_1)=m(x-x_1)` we will get

`(y-2)=-2(x-6)`

Therefore,option 2 and option 6 are correct.