Question

What is the slope of a line passing through points (2,3) and (4,1)?

Answer 1

-1

Answer 2

Can you show how you got the -1 Sharon504?

Answer 3

For points \((x_1, y_1) \) and \((x_2, y_2) \),

the slope of the line that passes through them is

\(slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} \)

Answer 4

Subtract the y-coordinates and write the difference in the numerator.
Subtract the x-coordinates and write the difference in the denominator.
That fraction is the slope. The fraction may be reduced if necessary.

Answer 5

Also, it doesn't matter in which order you subtract the x-coordinates and y-coordinates, but the two subtraction must be in the same order.

Answer 6

3-1/2-4
2/-2
-1

Answer 7

If you subtract the coordinates of the first point from the coordinates of the second point you get:

\(m = \dfrac{1 - 3}{4 - 2} =\dfrac{-2}{2}= -1\)

If you subtract the coordinates of the second point from the coordinates of the first point you get:

\(m = \dfrac{3 - 1}{2 - 4} =\dfrac{2}{-2}= -1\)

As you can see, the point you pick as the first point, and the point you pick as the second point do not alter the result. The slope comes out -1 either way.

Answer 8

Thanks mathstudent55 and sharon504. I now understand!

Answer 9

What you cannot do is subtract one set of coordinates one way and the other set the other way.

For example if you subtract the y-coordinates by subtracting the first coordinate from the second, and the when you do the x-coordinates you change the order and subtract the second coordinate from the first coordinate, then the slope will be incorrect.

\(\color{red}{This~is~incorrect:} ~~~~~ \color{green}{m = \dfrac{1 - 3}{2 - 4} = \dfrac{-2}{-2} = 1}\)

As you can see, by mixing the order of the subtractions, the slope came out 1 instead of -1, and is wrong.