Video Transcript
In this figure, the slope of the line between 𝐴 and 𝐵 is what. Is it option (A) undefined? Option (B) zero. Option (C) negative. Or is it option (D) positive?
In this question, we are given a figure containing a triangle 𝐴𝐵𝐶 in the coordinate plane and asked to use the figure to determine which option correctly describes the slope of the line between 𝐴 and 𝐵. We can begin by noting that we are not asked to find the exact slope of the line. Instead, we need to determine its sign or determine if it’s undefined.
We can recall that the slope of a line gives us information about the steepness of the line and the direction of the line. We can also recall that the slope of a line is defined by the change in the 𝑦-coordinates of two points on the line divided by the change in 𝑥-coordinates. So, a line that slopes upwards from left to right will have a positive slope. A line that slopes downwards from left to right will have a negative slope. A horizontal line has no change in the 𝑦-coordinates of points on the line, so the slope of any horizontal line is zero. Finally, if a line is vertical, then there is no change in the 𝑥-coordinates of points on the line. So the slope will be undefined.
If we look at the given figure, we can see that the line between 𝐴 and 𝐵 slopes downwards as we move from left to right. Since the line slopes downwards from left to right, we can say that the slope of the line between 𝐴 and 𝐵 is negative.
It is worth noting that we can also find various lines that do satisfy all of the other types of slope. For instance, the line between the origin and 𝐴 is vertical, so its slope is undefined. The line between 𝐵 and 𝐶 is horizontal, so its slope is zero. And the line between 𝐴 and 𝐶 slopes upwards from left to right, so its slope is positive. However, we can say that in the given figure, the slope of the line between 𝐴 and 𝐵 is negative, which is option (C).
