# Question #a8d79

Oct 16, 2017

$y = \frac{1}{2} x$

#### Explanation:

there are several ways of doing this.

we can use

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

where

$m = \text{ the gradient } = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$\left({x}_{1} , {y}_{1}\right) \text{ is a known coordinate on the line}$

we have

$m = \frac{1 - 0}{2 - 0} = \frac{1}{2}$

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$\implies y - 0 = \frac{1}{2} \left(x - 0\right)$

$\therefore y = \frac{1}{2} x$

or

$2 y - x = 0$

Oct 16, 2017

$\therefore y = \frac{1}{2} x$

#### Explanation:

Find the gradient $\textcolor{\pi n k}{m}$ of the line by using the formula $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

$\frac{1 - 0}{2 - 0} = \frac{1}{2}$

Using the equation $y - {y}_{1} = \textcolor{\pi n k}{m} \left(x - {x}_{1}\right)$, substitute the values of one pair of coordinates.

$y - 1 = \frac{1}{2} \left(x - 2\right)$
$\therefore y = \frac{1}{2} x$