The points of data are plotted: point A is at (4,-3) and point B is 5 units in the positive y direction. How would you describe the slope of this line?
The slope of this line cannot be determined with the given information. Only two points on the line are provided, and they do not give enough information to calculate the slope. The slope of a line is determined by the change in y-coordinates divided by the change in x-coordinates between any two points on the line.
To describe the slope of a line, we need to calculate the change in y-coordinates divided by the change in x-coordinates between two points on the line.
The slope, denoted as "m", can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
In this case, we have point A at (4, -3) and point B, which is 5 units in the positive y-direction from point A.
To find point B, we add 5 units to the y-coordinate of point A. Since point A is at (4, -3), point B would be at (4, -3 + 5) = (4, 2).
Substituting the coordinates (x₁, y₁) = (4, -3) and (x₂, y₂) = (4, 2) into the slope formula, we get:
m = (2 - (-3)) / (4 - 4)
m = (2 + 3) / 0
However, we encounter a division by zero situation, which means the slope is undefined. Therefore, the line is vertical and does not have a specific slope.
To describe the slope of the line passing through points A and B, we first need to find the coordinates of point B. Since point B is 5 units in the positive y direction from point A, we can determine its y-coordinate by adding 5 to the y-coordinate of point A.
Given that point A is at (4, -3), adding 5 units to the y-coordinate results in point B being located at (4, -3+5), which simplifies to (4, 2).
Now that we have the coordinates of both points, we can calculate the slope of the line using the slope formula:
Slope (m) = (y2 - y1) / (x2 - x1)
Let's substitute the values:
Slope (m) = (2 - (-3)) / (4 - 4)
Simplifying further:
Slope (m) = (2 + 3) / 0
Since the denominator is zero, we know that the slope is undefined.
Therefore, we can describe the slope of this line as undefined.