Two 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?
zero slope
positive slope
negative slope
undefined slope
The slope of this line is undefined.
To determine the slope of a line, we need two points on that line. In this case, we have two points: A(4, -3) and B, which is located 5 units in the positive y direction from A. Since the x-coordinate remains the same, the coordinates of point B would be (4, 2) since it moved 5 units upward from (4, -3).
To find the slope of the line passing through points A and B, we use the formula:
slope = (change in y)/(change in x)
Substituting the coordinates into the formula, we get:
slope = (2 - (-3))/(4 - 4)
simplify:
slope = (2 + 3)/(0)
Since we have a division by zero (0 in the denominator), this means that the slope is undefined.
Therefore, the correct answer is: undefined slope.
To determine the slope of a line, we need to calculate the change in y divided by the change in x between two points. In this case, we have two points: A(4, -3) and B, which is 5 units in the positive y direction from point A.
To find the change in y, we subtract the y-coordinates of the two points:
change in y = y-coordinate of B - y-coordinate of A
change in y = (0 - (-3))
change in y = 3
To find the change in x, we subtract the x-coordinates of the two points:
change in x = x-coordinate of B - x-coordinate of A
change in x = (4 - 4)
change in x = 0
Now, we can calculate the slope by dividing the change in y by the change in x:
slope = change in y / change in x
slope = 3 / 0
However, division by zero is undefined in mathematics. So, in this case, the slope is undefined.
Therefore, the correct answer is: undefined slope.