$y = 9x - 5$
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 the 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 $y = 9x$, the slope is $9$. This will also be the slope for our unknown line. We are given the point $(0, -5)$ and our slope $m = 9$. 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: $y - (-5) = 9(x - 0)$ Use distribution to simplify: $y + 5 = 9x - (9)(0)$ Simplify by multiplying: $y + 5 = 9x$ To change this equation into point-intercept form, we need to isolate $y$. To isolate $y$, we subtract $5$ from each side of the equation: $y = 9x - 5$ Now, we have the equation of the line in slope-intercept form.