What happens to the value obtained for the slope if the coordinates of the two ordered pairs aren't subtracted in the same order? what is an example.

All I know is that you would get the wrong slope for the ordered pairs, I do not know why. Can anyone help?

Correct slope = m = (y2-y1)/(x2-x1) = (y1-y2)/(x1-x2)

for a line between (x1,y1) and (x2,y2)

If the y2-y1 in the numerator is not consistent with the x2-x1 in the denominator, you get the wrong sign for the slope. For example,
(y2-y1)/(x1-x2) = -m

thanks now I know exactly what the situation is.

When finding the slope of a line, it is important to subtract the coordinates in a specific order. The typical convention is to subtract the y-coordinate of the second point from the y-coordinate of the first point, and subtract the x-coordinate of the second point from the x-coordinate of the first point.

Let's say we have two ordered pairs: (x1, y1) and (x2, y2), where (x1, y1) represents the coordinates of the first point and (x2, y2) represents the coordinates of the second point.

The formula for the slope of a line is given by:

m = (y2 - y1) / (x2 - x1)

By subtracting the coordinates in the same order, we ensure that the change in y-values is divided by the change in x-values for the same pair of points. This gives us the correct ratio and direction of how the line moves.

If we were to subtract the coordinates in a different order, let's say (y1 - y2) / (x1 - x2), it would yield a different value for the slope. This is because the change in y-values and change in x-values would not correspond to the same points on the line.

For example, let's consider two points: A(2, 5) and B(4, 9), using the convention of subtracting in the correct order:

m = (9 - 5) / (4 - 2) = 4 / 2 = 2

Now, if we were to subtract in the opposite order:

m' = (5 - 9) / (2 - 4) = -4 / -2 = 2

Although m and m' have the same numerical value, they have different signs, indicating different directions of the line. This is because we are essentially considering opposite slopes, resulting in a different interpretation of the line's behavior.

Therefore, it is crucial to subtract the coordinates in the correct order to find the correct slope and accurately represent the relationship between the two points on the line.