Question

What is the slope of the line through points (0,0) and (5,10)?

Answer 1

`m =2`

Explanation:

The slope of a line is defined as `"vertical change"/"horizontal change"`

In maths we usually write this as `m = (Delta y)/(Delta x)`, or informally as `"rise"/"run"`

If you regard `(0,0)` as the point of reference, you will see that the other point has a y-value of 10, and an x-value of 5.

These values indicate the changes have that have happened without us having to do any work.

From 0 to 10 is a change of 10
From 0 to 5 is a change of 5

`m = 10/5 = 2`

We can also use the formula `m = (y_2-y_1)/(x_2-x_1)`

`m = (10-0)/(5-0) = 10/5 = 2`

A slope of 2, or "2 in 1" means that every horizontal unit (to the right) has 2 vertical units (upwards) associated with it.