Question

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

Answer 1

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:
`2x+y=-2`
`2(2)+y=-2`
`4+y=-2`
`y=-2-4`
`y=-6`

So the first coordinate is `[2,-6]`

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

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

Answer 2

`"see explanation"`

Explanation:

`color(blue)"finding the intercepts"`

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

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

`x=0to0+y=-2toy=-2larrcolor(red)" y-intercept"`

`y=0to2x+0=-2tox=-1larrcolor(red)" x-intercept"`

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