What happens to the value obtained for the slope if the coordinates of the two ordered pairs aren't subtracted in the same order? Can you give an example?
e.g.
A(4,6)
B(9,-1)
slope AB = (-1-6)/(9-4) = -7/5 or -(7/5)
slope BA = (6+1)/(4-9) = 7/-9 or -(7/9)
notice that as long as I am consistent in the order that I subtract, I do get the correct answer.
Of course, by definition, slope = the y's / the x's , that obviously has to stay the same.
so by lining ab and ba up you take the #'s (1&6) to use them together?
the numerator of the slope value is always the difference of the y values, the denominator is always the difference of the x values.
The important thing is that you subtract in the same direction.
That is, if you take the first y - the second y, then you have to take the first x - the second x, and vice versa.
When subtracting the coordinates of two ordered pairs to find the slope, the order in which the subtraction is performed does affect the value obtained. Generally, the slope is calculated by subtracting the y-coordinates and then dividing by the difference of the x-coordinates.
Let's say we have two ordered pairs, (x1, y1) and (x2, y2). The slope formula is as follows:
slope = (y2 - y1) / (x2 - x1)
If you subtract the y-coordinates of the two ordered pairs in one order and the x-coordinates in a different order, you will end up with a different value for the slope.
For example, let's take the ordered pairs (2, 4) and (6, 8). If we subtract the y-coordinates first, we get:
slope = (8 - 4) / (6 - 2) = 4 / 4 = 1
Now, let's swap the subtraction order for the x-coordinates:
slope = (4 - 8) / (2 - 6) = -4 / -4 = 1
In this case, irrespective of the order of subtraction, we obtain the same value for the slope, which is 1. However, this is not always the case. Consider another example:
Take the ordered pairs (4, 7) and (2, 5). If we subtract the y-coordinates first:
slope = (5 - 7) / (2 - 4) = -2 / -2 = 1
Now, let's swap the subtraction order for the x-coordinates:
slope = (7 - 5) / (4 - 2) = 2 / 2 = 1
In this example, even though the subtraction orders were swapped, we still obtain the same value for the slope, which is 1.