Please Help Urgent!! Draw the graphs of 4x + 2y = 8 and 2x + 5y = 10. Shade the region bounded by these lines and y-axis. Find the area of shaded region.
Answers
Given:
The equations of lines 4x + 2y = 8 and 2x + 5y = 10
To find:
Draw the graphs of 4x + 2y = 8 and 2x + 5y = 10. Shade the region bounded by these lines and y-axis. Find the area of shaded region.
Solution:
From given, we have,
The equations of lines 4x + 2y = 8 and 2x + 5y = 10
The graph of equations of lines 4x + 2y = 8 and 2x + 5y = 10 and the y-axis is attached below.
The area of the shaded portion represents a triangle.
The area of a triangle with 3 points is given by,
Area of triangle = | [x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)] / 2 |
Consider the attached graph while going through the following steps.
A = (x1, y1) = (0, 4)
B = (x2, y2) = (0, 2)
C = (x3, y3) = (1.25, 1.5)
Area of triangle = | [0 (2 - 1.5) + 0 (1.5 - 4) + 1.25 (4 - 2)] / 2 |
= | [0 + 0 + 1.25 (2)] / 2 |
= | 2.5 / 2 |
= 1.25
Therefore, the area of triangle = 1.25 sq units.
