Answer:
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 \(m=\frac{y_2-y_1}{x_2-x_1}\)
Here, \({x_1=4,y_1=6,x_2=6,y_2=2\)
On substituting the values we will get \(m=\frac{2-6}{6-4}=-2\)
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.
