a. Given:
y = 2x and y = -x/2 + 5
The line y = 2x is line passing through origin (0,0)
The line y = -x/2 + 5 is line that has intercepts (0,5) and (10,0)
The point of intersection of two lines are given by:
Substitute y = 2x in second equation:
2x = -(x/2) + 5
=>2x + (x/2) = 5
=>(4x + x) = 10
=>5x = 10
=>x = 10/5 = 2
Hence, y = 2x = 2(2) = 4
The point of intersection is given by (2,4)
b.
We need to find the following area in the graph:
Concept Used:
The area of a triangle is given by:
A = (1/2)(base length)(height)
Calculation for Area:
Height of the triangle (as we see in the graph) is the distance between the point (2,4) and (2,0)
The distance between these two points is (4-0) = 4
Thus, height of triangle = 4
The base length = 10 (from graph)
Hence,
Area of triangle = (1/2)(10)(4) = 20 units
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