To Draw the line of reflection for the given point, we can just draw a line that passes through both points.
Here is what we get:
So this is the line of reflection. To find its equation, we first start at the standard line equation form:
[tex]y=ax+b[/tex]
Know we use the points given to find out "a", and "b". So:
[tex]\begin{gathered} 2=a+b \\ 5=4a+b \end{gathered}[/tex]
If we substract the first from the second, we eliminate "b", and thus we find "a":
[tex]\begin{gathered} 5-2=4a+b-(a+b)=4a-a+b-b=3a \\ 3=3a \\ a=1 \end{gathered}[/tex]
Now we put "a" into either equations, let's use the first one:
[tex]\begin{gathered} 2=1+b \\ b=2-1 \\ b=1 \end{gathered}[/tex]
So, the line of reflection equation is:
[tex]y=x+1[/tex]
