They y-intercept of a line L is 4. If the slope of L is negative, which of the following could be the x-intercept of L?

I. -1
II. 0
III. 6

A I only
B II only
C III only
D I and II
E I and III


ans C.
i have no idea how to answer this question. please help me understand.
thanks.

The easiest way to approach this one is to visualize it. The slope is negative, meaning it goes downhill from left to right. It crosses the y-axis at 4. That means that (0,4) is a point on the line.

If the x-intercept is -1, then we have a line that slopes upward from left to right, and thus has a positive slope.
If the x intercept is 0, we have a vertical line, which doesn't have a negative slope.
If the x-intercept is anything positive (like 6) then we have a line that slopes downward, so this is our only viable option.

Veritas Help

thanks. that makes sense.

how about algebraically how do you solve this question?

It will be a slightly slower approach, but you could plug in the two points we know in each situation and then find the slope of the line created from those two points.

The point they give us originally is (0,4)

The other points are
I. (-1,0)
II. (0,0)
III. (6,0)

Then use y2-y1 / x2-x1 to arrive at m, or the slope.

Veritas Help

thanks. that helps.