Problem Solving

VJesus12 wrote:Line \(D\) passes through the point \((-2,5),\) and the product of its \(x\)-intercept and \(y\)-intercept is positive. Which of the following points could be on the line \(D?\)

A. \((5,10)\)
B. \((-3,2)\)
C. \((-1,7)\)
D. \((-1,2)\)
E. \((-3,1)\)

[spoiler]OA=D[/spoiler]

Source: Veritas Prep

A necessary condition for a line having a positive product by multiplying its two intercepts is that the line has a negative slope. So we need to determine which point in the answer choices and the given point (-2, 5) will yield a negative slope for line D.

A) (5, 10)

m = (10 - 5)/(5 - (-2)) = 5/7

This is not negative.

B) (-3, 2)

m = (2 - 5)/(-3 - (-2)) = (-3)/(-1) = 3

This is not negative.

C) (-1, 7)

m = (7 - 5)/(-1 - (-2)) = 2/1 = 2

This is not negative.

D) (-1, 2)

m = (2 - 5)/(-1 - (-2)) = -3/1 = -3

This IS negative.

E) (-3, 1)

m = (1 - 5)/(-3 - (-2)) = (-4)/(-1) = 4

This is not negative.

Answer: D