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24 Mar 2022, 01:30
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A
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Difficulty:
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Question Stats:
52% (01:43) correct
49%
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What is the X intercept of non horizontal line m?
(1) The slope of m is 4 times the y intercept of m
(2) The y intercept of line m is -2.
Are You Up For the Challenge: 700 Level Questions
(1) The slope of m is 4 times the y intercept of m
(2) The y intercept of line m is -2.
Are You Up For the Challenge: 700 Level Questions
24 Mar 2022, 08:07
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Bunuel
What is the x intercept of non-horizontal line m?
(1) The slope of m is 4 times the y-intercept of m
(2) The y intercept of line m is -2.
(1) The slope of m is 4 times the y-intercept of m
(2) The y intercept of line m is -2.
Target question: What is the x-intercept of non-horizontal line m?
Awesome question!!
Statement 1: The slope of m is 4 times the y intercept of m
Let's let y = Mx + b be the equation of line m, where M = the slope of line m, and b = the y-intercept of a line m.
Since b is the y-intercept of line m, then the statement that tells us that 4b is the slope of line m.
So, the equation of line m becomes: y = 4bx + b
Important concept #1: The x-intercept of a line is the x-value that corresponds to y = 0 (since y = 0 for all points on the x-axis)
So, to find the x-intercept, we'll replace y with 0 and solve the following equation for x: 0 = 4bx + b
Factor the right side: 0 = b(4x + 1)
So, EITHER b = 0 OR 4x + 1 = 0.
Important concept #2: Since the question tells us that line m is NOT horizontal, we know that the slope of the line cannot be zero.
In the equation y = 4bx + b, the slope of the line is 4b, which means 4b cannot equal 0, which means b cannot equal 0.
So, it must be the case that: 4x + 1 = 0
Solve for x by subtracting 1 from both sides: 4x = -1
Solve : x = -1/4, which means the answer to the target question is the x-intercept of line m is -1.4
[Note: On test day, I wouldn't waste time solving 4x + 1 = 0, since it's clear that the equation will have only one possible solution]
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The y-intercept of line m is -2.
All this tells us is that line m passes through the point (0, -2)
There are infinitely-many lines that can be drawn through the point (0, -2)
For example, line m could look like this....
...in which case the answer to the target question is the x-intercept of line m is 1
Conversely, line m could look like this....
...in which case the answer to the target question is the x-intercept of line m is -3
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
General Discussion
24 Mar 2022, 19:20
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What is the X intercept of non horizontal line m?
Stat1: The slope of m is 4 times the y intercept of m
Equation of st. line ; y = mx +b, y intercept means, put x = 0 then y= b and we have now m = 4b
Now the equation is y= 4bx +b. To get x intercept, put y = 0, then x = -1/4. Sufficient
Stat2: The y intercept of line m is -2.
y intercept means, put x = 0 then y= -2. We have no idea of slope, m. Not Sufficient
So, I think A.
Stat1: The slope of m is 4 times the y intercept of m
Equation of st. line ; y = mx +b, y intercept means, put x = 0 then y= b and we have now m = 4b
Now the equation is y= 4bx +b. To get x intercept, put y = 0, then x = -1/4. Sufficient
Stat2: The y intercept of line m is -2.
y intercept means, put x = 0 then y= -2. We have no idea of slope, m. Not Sufficient
So, I think A.
