# How do you graph using the intercepts for 2x-4y=42?

May 10, 2018

$x$-intercept: $\left(21 , 0\right)$
$y$-intercept: $\left(0 , - \setminus \frac{21}{2}\right)$

#### Explanation:

Be definition, a coordinate axis is defined as the sets of points where the other coordinate is zero, i.e.:

$x$-axis: $\left\{\left(x , y\right) \setminus \in \setminus m a t h {\boldsymbol{R}}^{2} : y = 0\right\}$

$y$-axis: $\left\{\left(x , y\right) \setminus \in \setminus m a t h {\boldsymbol{R}}^{2} : x = 0\right\}$

So, the line intercepts the $x$-axis where $y = 0$, i.e.

$2 x - 4 \setminus \cdot 0 = 42 \setminus \iff 2 x = 42 \setminus \iff x = 21$

So, the point is $\left(21 , 0\right)$

As for the $y$-axis, we must impose $x = 0$:

$2 \setminus \cdot 0 - 4 y = 42 \setminus \iff - 4 y = 42 \setminus \iff y = - \setminus \frac{42}{4} = - \setminus \frac{21}{2}$

So, the point is $\left(0 , - \setminus \frac{21}{2}\right)$