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

Question

1512 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-10T07:33:14

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

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

$x$ -axis: ${(x,y) \in \mathbb{R}^2 : y = 0}$

$y$ -axis: ${(x,y) \in \mathbb{R}^2 : x = 0}$

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

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

So, the point is $(21,0)$

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

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

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

How do you graph using the intercepts for 2x-4y=422x-4y=42?