Stuck on this one:

find the slope of the line passing through each pair of points or stat that the slope is undefined. assume that all variables represent positive real numbers. then indicate whether the line through the points rises, falls, is horizontal or is vertical
(0,a) and (b,0)

slope = -a/b

the rest of your question can only be answered if we know that values of a and b

Thank you. That is all that was written in the book.

To find the slope of the line passing through the points (0, a) and (b, 0), you can use the slope formula:

slope = (y2 - y1) / (x2 - x1)

Let's label the coordinates:
Point 1: (x1, y1) = (0, a)
Point 2: (x2, y2) = (b, 0)

Now, substitute the values into the slope formula:

slope = (0 - a) / (b - 0)
slope = -a / b

If the denominator (b - 0) is not zero, then the slope will be defined. However, if the denominator is zero, the slope will be undefined.

Looking at the denominator, b - 0, we can see that it will not be zero as long as b is not zero. Since it is given that all variables represent positive real numbers, we can assume that b is not zero.

Thus, the slope is defined and given by -a / b.

Now, let's analyze the slope to determine if the line rises, falls, is horizontal, or vertical:

If the slope is positive, the line rises.
If the slope is negative, the line falls.
If the slope is zero, the line is horizontal.
If the slope is undefined, the line is vertical.

In this case, the slope is -a / b, and since a and b are both positive real numbers, we do not have enough information to determine the sign of the slope.

Therefore, we cannot determine whether the line rises, falls, is horizontal, or vertical based on the given coordinates (0, a) and (b, 0).