Given the boundaries of the area to be found are,
• The line equation is 2y = 5x + 7
• The y= 0, x-axis
• x = 2 (a line parallel toy-axis)
• x = 8 (a line parallel toy-axis)
As per the given boundaries,
• The line 2y = 5x + 7.
• x=2 is parallel toy-axis at 2 units away from the y-axis.
• x=8 is parallel toy-axis at 8 units away from the y-axis.
• y = 0, the x-axis.
• The four boundaries of the region to be found are,
•Point A, where the line 2y = 5x + 7 and x=2 meet.
•Point B, where the line 2y = 5x + 7and x=8 meet.
•Point C, where the x-axis and x=8 meet i.e. C(8,0).
•Point D, where the x-axis and x=2 meet i.e. D(2,0).
The line equation 2y = 5x + 7 can be written as,
y = \(\frac{5x+7}{2}\)
Area of the required region = Area of ABCD.
The Area of the required region = 96 sq. units.
