Answer
$3x + y = - 1$
Work Step by Step
We know that parallel lines have the exact same slope.
The line we are given is written in the slope intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Therefore, the slope of the line we are given is $-3$, which is the same as the slope of the line we are looking for.
Since we have the slope and we have a point on that line, we should use the point-slope form to find the line's equation. The point-slope form is given by:
$$y - y_{1} = m(x - x_{1})$$
The point we are given is $(0, -1)$. Let's plug the $x$ and $y$ values of this point, together with the slope $-3$, into the point-slope form:
$$y - (-1) = -3(x - 0)$$
Let's distribute on the right and simplify on the left:
$$y + 1 = -3x + 0$$
We want the equation in standard form, which is $Ax + By = C$. So, we have to move the $x$ term to the left by adding $3x$ to both sides:
$$3x + y + 1 = 0$$
Now we subtract $1$ from both sides of the equation to get the constant on the right side:
$$3x + y = - 1$$
Now, we have the equation of the line in standard form.
