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

Feb 8, 2017

$m = 2$

Explanation:

The slope of a line is defined as $\text{vertical change"/"horizontal change}$

In maths we usually write this as $m = \frac{\Delta y}{\Delta x}$, or informally as $\text{rise"/"run}$

If you regard $\left(0 , 0\right)$ 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

$m = \frac{10}{5} = 2$

We can also use the formula $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{10 - 0}{5 - 0} = \frac{10}{5} = 2$

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