CRITICAL THINKING Explain how you know that the slope of the line through
(4, 5) and (4, 5) is positive without calculating.
without "calculating", I can tell that the question is bogus, since only one point is given.
Can't find slope if given only one point.
To determine whether the slope of a line is positive without calculating, we need to understand the concept of slope and the relationship between the x-coordinates and y-coordinates of the given points.
Slope is a measure of how steep a line is. It is defined as the change in the y-coordinate divided by the change in the x-coordinate. Mathematically, the slope (m) is given by the formula:
m = (Δy / Δx)
Where Δy represents the change in y-coordinates and Δx represents the change in x-coordinates between two points on the line.
In this case, we are given the points (4, 5) and (4, 5). Since both points have the same x-coordinate (4), the change in x (Δx) is equal to 0. Because division by zero is undefined, we cannot calculate the slope.
However, we can still determine whether the slope is positive or not by looking at the overall pattern. In this case, both points have the same y-coordinate as well (5). Since there is no change in y (Δy = 0) and the change in x is 0 (Δx = 0), this means that the line is perfectly horizontal.
Since a horizontal line has a slope of 0 (it neither rises nor falls), we can conclude that the slope of the line through the points (4, 5) and (4, 5) is 0, which is neither positive nor negative.