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In the xy-coordinate system, line k has y-intercept 12 and an x-intercept greater than zero. If the area of the triangular region enclosed by line k and the two axes is 30, what is the slope of line k?
Title
Bounded triangle
Your Result
Correct
Difficulty
Hard
Your Pace
0:02
Others' Pace
1:57
Video Explanation
Text Explanation
We know that the area of a triangle = (base) (height). We also know that the triangle's height is 12, since the y-intercept is 12. So setting x = base:
30 = (x)(12)
30 = 6x
x = 5
The base of the triangle is 5, which means that the x-intercept must be (5,0). Here's a visual of all the information we now have:
So we know two points exist on line k: (0, 12) and (5, 0). We can use these to find the slope using the formula:
Answer: (A)
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