Problem Solving

Pawan Ramnani wrote:What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?

a) 8
b) 10
c) 12
d) 14
e) 18

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First, let's graph the lines y = 1 and x = 1


At this point, we need to find the points where the line y = 6-x INTERSECTS the other two lines.

For the vertical line, we know that x = 1, so we'll PLUG x = 1 into the equation y = 6-x to get y = 6-1 = 5
Perfect, when x = 1, y = 5, so one point of intersection is (1,5)

For the horizontal line, we know that y = 1, so we'll PLUG y = 1 into the equation y = 6-x to get 1 = 6-x. Solve to get: x = 5
So, when y = 1, x = 5, so one point of intersection is (5,1)

Now add these points to our graph and sketch the line y = 5-x


At this point, we can see that we have the following triangle.

The base has length 4 and the height is 4
Area = (1/2)(base)(height)
= (1/2)(4)(4)
= 8

Answer: A