Sketch the region enclosed by the graphs of x = 0, 6y - 5x = 0 and x + 3y = 21. Find the area.

Solution:

Given x = 0, 6y - 5x = 0 and x + 3y = 21

Take some sample values of x,y and plot the graph

The horizontal axis is the x-axis and the vertical axis is the y-axis

The blue line is 6y - 5x = 0 and the green line is x + 3y = 21

Hence, we need to find the area of the shaded portion and it forms a triangle

The height is 5 units(i.e. Distance between the lines intersection point to the y-axis)

The base is 7 units (i.e.distance from origin to green straight line intersecting y-axis)

Area of a triangle is given by (base * height)/2

Area = (5*7)/2

Area = 35/2

Area = 17.5 sq. units

Therefore, the area between the lines is 17.5 sq.units

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Sketch the region enclosed by the graphs of x = 0, 6y - 5x = 0 and x + 3y = 21. Find the area.

Summary:

The region enclosed by the graphs of x = 0, 6y - 5x = 0 and x + 3y = 21 is sketched and the area is 17.5 sq.units.