How do you graph 2x+y=-2 using intercepts?

May 29, 2017

Find two vaules for $x$ and $y$ that solve the equation, sketch them on a graph, and draw a line going through both points.

Explanation:

The easiest method is by finding two coordinates.
Find two vaules for $x$ and $y$ that solve the equation, sketch them on a graph, and draw a line going through both points.

To find a co-ordinate, we must pick any $x$, or any $y$.

Let's pick $x = 2$.

Then substitute into the equation:
$2 x + y = - 2$
$2 \left(2\right) + y = - 2$
$4 + y = - 2$
$y = - 2 - 4$
$y = - 6$

So the first coordinate is $\left[2 , - 6\right]$

Then repeat picking a different $x$ or $y$ value.
Assume $y = 7$
$2 x + y = 7$
$2 x + 7 = 7$
$2 x = 0$
$x = 0$
Second coordinate: $\left[0 , 7\right]$

Then simply sketch a line between $\left[2 , - 6\right]$ and $\left[0 , 7\right]$
graph{2x+y=-2 [-17.81, 17.81, -8.9, 8.91]}

May 29, 2017

$\text{see explanation}$

Explanation:

$\textcolor{b l u e}{\text{finding the intercepts}}$

• " let x = 0, in the equation for y-intercept"

• " let y = 0, in the equation for x-intercept"

$x = 0 \to 0 + y = - 2 \to y = - 2 \leftarrow \textcolor{red}{\text{ y-intercept}}$

$y = 0 \to 2 x + 0 = - 2 \to x = - 1 \leftarrow \textcolor{red}{\text{ x-intercept}}$

$\text{plot these 2 points and draw a straight line through them}$
graph{-2x-2 [-10, 10, -5, 5]}