Solution
You can use this fact to examine the information given in the first two statements. Remember that you need to evaluate each statement by itself.
Choice A states that the x-intercept is twice the y-intercept, so you can conclude that both intercepts have the same sign, and thus the slope of line k is negative. So the information in Choice A is sufficient to determine that the slope of line k is negative.
Choice B states that the product of the x-intercept and the y-intercept is positive. You know that the product of two numbers is positive if both factors have the same sign. So this information is also sufficient to determine that the slope of line k is negative.
Choice C, it is helpful to recall the definition of the slope of a line passing through two given points. You may remember it as “rise over run.”
If the two points are (a, b) and (r, s), then the slope is \(\frac{b-s}{a-r}\)
Choice C states that the product of the quantities (a−r) and (b−s) is negative. Note that these are the denominator and the numerator, respectively, of \(\frac{b-s}{a-r}\), the slope of line k. So you can conclude that (a−r) and (b−s) have a−r opposite signs and the slope of line k is negative. The information in Choice C is sufficient to determine that the slope of line k is negative.
So each of the three statements individually provides sufficient information to determine whether the slope of line k is negative.
The correct answer are \(A, B, and C\).
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