Answer:
Option 2 and option 6 are correct which is [tex](y-6)=-2(x-4)[/tex] and [tex](y-2)=-2(x-6)[/tex] 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
[tex](y-y_1)=m(x-x_1)[/tex]
Where [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex]{x_1=4,y_1=6,x_2=6,y_2=2[/tex]
On substituting the values we will get [tex]m=\frac{2-6}{6-4}=-2[/tex]
Now, substituting values in [tex](y-y_1)=m(x-x_1)[/tex] we will get
[tex](y-6)=-2(x-4)[/tex]
If we choose [tex]x_1=6,y_1=2,x_2=4,y_2=6[/tex] then substituting the values in [tex](y-y_1)=m(x-x_1)[/tex] we will get
[tex](y-2)=-2(x-6)[/tex]
Therefore,option 2 and option 6 are correct.
