Question

What is the slope of the line that runs through points (1,-5) and (5, 10)?

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)(10) - color(blue)(-5))/(color(red)(5) - color(blue)(1)) = (color(red)(10) + color(blue)(5))/(color(red)(5) - color(blue)(1)) = 15/4`

Answer 2

`5/3`

Explanation:

To find the slope, we need to use the, creatively named, Point-Slope Formula, which uses, wait for it, two points to find the slope

The form is `(y_2-y_1)/(x_2-x_1)`, based on `(x_1, y_1)` and `(x_2, y_2)`.

So, we have `(1, -5)` and `(5, 10)`. That gives us `(10--5)/(10-1)`, or `15/9`, which simplifies to `(5*cancel(3))/(3*cancel(3))`: `5/3`. That's our slope