Given:
[tex]\begin{gathered} f(x)=2x+1 \\ x=3 \end{gathered}[/tex]
Parallel line slope are also same then parallel line equation is:
[tex]f(x)=2x+k[/tex]
The line pass (2,7) then:
[tex]\begin{gathered} f(x)=2x+k \\ 7=2(2)+k \\ 7=4+k \\ k=7-4 \\ k=3 \end{gathered}[/tex]
So two parallel line equation is :
[tex]\begin{gathered} f(x)=2x+1 \\ f(x)=2x+3 \end{gathered}[/tex]
As the difference in y intrcepts is 2.
The side of parallelogram along y- axis is 2.
Two other parallel line are x=0 and x=3
so vertical distance between them is 3
so area is:
[tex]\begin{gathered} \text{Area}=2\times3 \\ =6 \end{gathered}[/tex]
