Say the y-intercept is (2 + p), where p is a positive numberssyohee wrote:1. If the y-intercept of a line is greater than 2, the x-intercept is greater than 3?
1) The line passes through (2, 3)
2) The slope of the line is 1/2
the answer is can anyone please explain why?
Thanks!
Let's make use of intercept form of the Straight line.
The standard form is:
x/a + y/b = 1; where a and b are x-intercept and y-intercept, respectively
We are given that b = 2 + p
Thus,
x/a + y/(2+p) = 1
We have to ensure whether a > 3.
Statement 1: The line passes through (2, 3).
Thus,
2/a + 3/(2+p) = 1
Let's plug-in a = x-intercept = 3 and see whether p, a positive number, is still positive.
Thus,
2/3 + 3/(2+p) = 1
3/(2+p) = 1/3
2 + p = 9
p = 7, a positive number
=> x-intercept is NOT greater than 3.
Let's try with a > 3; say a = 4
Thus,
2/4 + 3/(2+p) = 1
3/(2+p) = 1/2
2 + p = 6
p = 4, a positive number
=> x-intercept is greater than 3. No unique answer. Insufficient!
Statement 2: The slope of the line is 1/2.
Let's make use of slope and intercept form of the staright line.
Say the equation of the line is: y = mx + c; where m is the slope and c is y-intercept.
Thus,
y = x/2 + (2+p)
Say x-intercept = a, thus, we deduce that the line passes through the point (a, 0).
Thus,
0 = a/2 + (2 + p)
0 = a + 4 + 2p
a = -(4 + 2p)
=> x-intercept = |a| = |-(4 + 2p)| = 4 + 2p
Since p is a positive number x-intercept = |a| > 4 or greater than 3. Suffcient.
The correct answer: B
Hope this helps!
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-Jay
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