Draw the graphs of the equations x=3, x=5 and 2x-y-4=0. Also find the area of the quadrilateral formed by the lines and the X-axis.

Explanation

Given equation of lines 2x-y-4=0, x=3 and x=5
Table for line 2x-y-4=0,

`{:(" "x,0,2,),(y=2x-4,-4,0,),("Points","P","Q",):}`
draw the points P(0,-4) and Q(2, 0) and join these points and form a line PQ also draw the lines x=3 and x=5.

`:. `Area of quadrilateral `ABCD=(1)/(2)xx`distance between parallel lines `(AB)xx(AD+BC) " " `[since, quadrilateral ABCD is a trapezium]
`=(1)/(2)xx2xx(6+2) " " `[`:. AB=OB-OA=5-3=2, AD=2` and BC=6]
`" " `=8sq units
Hence, the required area of the quadrilateral formed by the lines and the X-axis is 8 sq units.