GRE Math Challenge Question
Q: What is the area enclosed in the coordinate plane by the x-axis, the y-axis, and the line with the equation y = −4x + 20?
A) 25
B) 40
C) 50
D) 75
E) 100
Explanation:
Correct Choice: (C)
The equation of the line is y = −4x + 20. This equation is in the slope-intercept form y = mx + b. So the y-intercept is 20. To find the x-intercept, we set y equal to 0.
Then since y = −4x + 20,
−4x + 20 = 0,
−4x = −20, and .
The x-intercept is 5.
We can draw a figure to make it easier to see the area enclosed.
The area enclosed is a right triangle with a leg of length 5 along the x-axis (the x-intercept is 5) and a leg of length 20 along the y-axis (the y-intercept is 20).
The area of any triangle is (1/2)× base × height. The area of a right triangle is × leg1× leg2, because one leg can be considered to be the base and the other leg can be considered to be the height.
The triangle of this question has legs of lengths 5 and 20. The area enclosed in the coordinate plane by the x-axis, the y-axis, and the line with the equation y = −4x + 20 is the area of this right triangle.
The area of this right triangle is . 1/2 * 5 * 20 = 5 * 10 = 50
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