Question

What is the slope of the line going through (5, -4) and (6, -2)?

Answer 1

See a solution process below:

Explanation:

The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

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

Substituting the values from the points in the problem gives:

`m = (color(red)(-2) - color(blue)(-4))/(color(red)(6) - color(blue)(5)) = (color(red)(-2) + color(blue)(4))/(color(red)(6) - color(blue)(5)) = 2/1 = 2`

Answer 2

Use the slope equation
The slope is `m=2`.

Explanation:

`m = ("change in " y)/("change in " x)`

The letter `m` is used to represent the slope.

Call one point `(x_1,y_1)` and the other point `(x_2,y_2)`

Then

`m = (y_2-y_1)/(x_2-x_1)`

So if `(5,-4)` is `(x_1,y_1)` and `(6,-2)` is `(x_2,y_2)`, then The slope equation states

`m = (y_2-y_1)/(x_2-x_1) = (-2-(-4))/(6-5) = 2/1= 2`

The slope equals two.