find the slope of the line through the folling pairs of points. (-5, -3) and (-5,2)
Since the two points are on a vertical line (how does one know that?), the slope is infinite.
To find the slope of a line given two points, we can use the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
In this case, we have the points (-5, -3) and (-5, 2).
To calculate the change in y-coordinates, we subtract the y-coordinate of the second point from the y-coordinate of the first point:
Change in y-coordinates = 2 - (-3)
= 2 + 3
= 5
To calculate the change in x-coordinates, we subtract the x-coordinate of the second point from the x-coordinate of the first point:
Change in x-coordinates = -5 - (-5)
= -5 + 5
= 0
The slope of a line is the ratio of the change in y-coordinates to the change in x-coordinates. However, in this case, we have a change in x-coordinates of 0, which means the line is vertical.
A vertical line has an undefined slope because the change in x is zero. Therefore, we can say that the slope of the line through the points (-5, -3) and (-5, 2) is infinite.