For each answer choice, ask yourself "Does this statement guarantee that line k has a positive slope?" If your reply is "Yes, the slope of line k must be positive if this statement is true" then select that answer choice.

Consider A and B. Drawing a figure like the one attached will help you evaluate these two statements. For lines with positive slope that avoid the origin, the x- and y-intercepts must have opposite signs. For lines with negative slope that avoid the origin, the intercepts must have matching signs. If one intercept is the negative reciprocal of the other, then one intercept must be negative and the other positive. The same is true if the product of the intercepts is negative. So if A or B is true, then the slope of line k must be positive.

Now consider C. This statement gives two points on line k and says that if you multiply the difference in their y-coordinates by the difference in their x-coordinates, you get a positive value. But wait. If you divide those differences, you get the slope of line k. So Plug (a, b) and (r, s) into the slope formula: slope = (b − s) ÷ (a − r)

If (a − r)(b − s) > 0, then either both differences are positive or both are negative. And if (a − r) and (b − s) yield differences with matching signs, then (b − s) ÷ (a − r) > 0, meaning the slope of line k must be positive. So if C is true, then the slope of line k must be positive.

A, B, and C are all correct.