Question

How do you graph `4x+y=-1` using intercepts?

Answer 1

Sub in the variables as `0` and solve for the other variable.

In this case, `x=-1/4` and `y=-1`.

Explanation:

All we have to do is sub in the variables as `0` and solve for the other variable.

`x`-intercept

Here, we are solving for the `x`-intercept. Thus, we have to sub `y=0`.

`4x+y=-1`

`4x+0=-1`

Now, let's bring like terms together and add them.

`4x=-1`

Now, we can isolate for `x`.

`(4x)/4=-1/4`

`x=-1/4`

Therefore, because `x=-1/4`, the `x`-intercept is `(-1/4,0)`.

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`y`-intercept

Now, if we're solving for the `y`-intercept, we would have to sub in `x=0`.

`4x+y=-1`

`4(0)+y=-1`

Now, we add like terms,.

`y=-1`

Therefore, because `y=-1`, the `x`-intercept is `(0, -1)`.

We can double check our work by graphing the equation:

graph{4x+y=-1 [-10, 10, -5, 5]}

As you can see, the intercepts on the graph match with what we solved for!

Hope this helps :)