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

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Answer 1 · 2017-05-28T19:07:22

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

In this case, $x = - \frac{1}{4}$ $x=-1/4$ and $y = - 1$ $y=-1$ .

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

$x$ $x$ -intercept

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

$4 x + y = - 1$ $4x+y=-1$

$4 x + 0 = - 1$ $4x+0=-1$

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

$4 x = - 1$ $4x=-1$

Now, we can isolate for $x$ $x$ .

$\frac{4 x}{4} = - \frac{1}{4}$ $(4x)/4=-1/4$

$x = - \frac{1}{4}$ $x=-1/4$

Therefore, because $x = - \frac{1}{4}$ $x=-1/4$ , the $x$ $x$ -intercept is $(- \frac{1}{4}, 0)$ $(-1/4,0)$ .

$y$ $y$ -intercept

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

$4 x + y = - 1$ $4x+y=-1$

$4 (0) + y = - 1$ $4(0)+y=-1$

Now, we add like terms,.

$y = - 1$ $y=-1$

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

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 :)

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