# How do you find the slope and intercept of x-2y=0?

Jan 14, 2016

Slope $= \frac{1}{2}$
y-intercept: $0$ (i.e. at $\left(0 , \textcolor{g r e e n}{0}\right)$
x-intercept: $0$ (i.e. at $\left(\textcolor{g r e e n}{0} , 0\right)$

#### Explanation:

For a linear equation in the general form:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{A} x + \textcolor{b l u e}{B} y = C$
the slope is given by the equation:
$\textcolor{w h i t e}{\text{XXX}} m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

In this case
$\textcolor{w h i t e}{\text{XXX")x-2y=0color(white)("XXX")rArrcolor(white)("XXX}} \textcolor{red}{1} x + \left(\textcolor{b l u e}{- 2} y\right) = 0$

and therefore
$\textcolor{w h i t e}{\text{XXX}} m = - \left(\frac{\textcolor{red}{1}}{\textcolor{b l u e}{- 2}}\right) = \frac{1}{2}$

The y-intercept is the value of $y$ when $x = \textcolor{c y a n}{0}$
$\textcolor{w h i t e}{\text{XXX}} \left(\textcolor{c y a n}{0} - 2 y = 0\right) \rightarrow \left(y = 0\right)$

The x-intercept is the value of $x$ when $y = \textcolor{\mathmr{and} a n \ge}{0}$
$\textcolor{w h i t e}{\text{XXX}} \left(x - 2 \left(\textcolor{\mathmr{and} a n \ge}{0}\right) = 0\right) \rightarrow \left(x = 0\right)$