Question

What is the slope of the line that passes through the pair of points `(-7/2, -3)` and `(-5, 5/2)`?

Answer 1

See a solution process below:

Explanation:

The formula for find the slope of a line is:

`m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `(color(blue)(x_1), color(blue)(y_1))` and `(color(red)(x_2), color(red)(y_2))` are two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(5/2) - color(blue)(-3))/(color(red)(-5) - color(blue)(-7/2))`

`m = (color(red)(5/2) + color(blue)(3))/(color(red)(-5) + color(blue)(7/2))`

`m = (color(red)(5/2) + color(blue)((2/2 xx 3)))/(color(red)((2/2 xx -5)) + color(blue)(7/2))`

`m = (color(red)(5/2) + color(blue)(6/2))/(color(red)(-10/2) + color(blue)(7/2))`

`m = (11/2)/(-3/2)`

`m = (11 xx 2)/(-3 xx 2)`

`m = -22/6`

`m = -11/3`