Answer
$y = 5x - 11$
Work Step by Step
We know that two parallel lines have the same slope, so if we are given the equation of a line parallel to the one we are looking for, then we know we already have the slope of our unknown line.
The known line is written in slope-intercept form, which is given by the formula:
$y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
So for our given line $y = 5x - 2$, the slope is $5$. This will also be the slope for our unknown line.
We are given the point $(2, -1)$ and our slope $m = 5$. We now have the slope and a point on our unknown line.
We can plug these values into the point-slope equation, which is given by the formula:
$y - y_1 = m(x - x_1)$
Let's plug in the points and slope into the formula:
$y - (-1) = 5(x - 2)$
Use distribution to simplify:
$y + 1 = 5x + 5(-2)$
Simplify by multiplying:
$y + 1 = 5x - 10$
To change this equation into point-intercept form, we need to isolate $y$. To isolate $y$, we subtract $1$ from each side of the equation:
$y = 5x - 10 - 1$
Add constants to simplify:
$y = 5x - 11$
Now, we have the equation of the line in slope-intercept form.
