A line passes through the point (4,0). Taken individually which of the following is sufficient to determine the slope? I listed all 3 answer choices - the x-intercept, the y-intercept and another point that goes through the line. The answer key said that the x-intercept is not sufficient, but the solutions video said that the x-intercept is sufficient. Can I please get some clarity? Thank you.
You can find the slope of a straight line as long as you have two distinct points.
The issue with the x-intercept in the question is clear if we take a look at the point given in the problem. (4, 0) is itself the x-intercept. So, if we only were to have (4, 0) and the x-intercept data of a straight line we would have the same point twice. One point is not enough to conclude the slope of a line.
The y-intercept and another point would be sufficient. It is strange that the solution video and answer key do not line up, though.
The video had a problem with different point, but same concept. I see now that the point in question was already the x-intercept, so giving the x-intercept is effectively giving the same point. Thanks for the answer!