Answer
$y = -3x - 1$
Work Step by Step
First, let's find the slope of the line given.
This line is written in slope-intercept form, which is given by the following formula:
$y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.
So the slope of this line is the coefficient of $x$; in this case, the slope of this line is $-3$.
Therefore, the slope of the line whose equation we want to find is also $-3$.
Let us plug this slope and the point we are given into the point-slope form of the equation, which is given by the formula:
$y - y_1 = m(x - x_1)$, where $m$ is the slope of the line and $(x_1, y_1)$ is a point on that line.
Let us use the point $(-1, 2)$ to plug into the formula:
$$y - 2 = -3(x - (-1))$$
Simplify the equation:
$$y - 2 = -3(x + 1)$$
We are asked to give the equation either in standard form or slope-intercept form. Let's rewrite this equation in slope-intercept form. First, we distribute the terms on the right side of the equation:
$$y - 2 = -3x - 3$$
Isolate $y$ by adding $2$ to each side of the equation:
$$y = -3x - 1$$
