Answer
$$y = -\frac{1}{5}x + 6$$
Work Step by Step
We already know the y-intercept of this line. So the next piece is to find the slope of the equation.
We know from the information given that the line whose equation we are looking for is perpendicular to the line with equation $y = 5x- 1$. In order for two lines to be perpendicular, the slopes must be negative reciprocals of one another. If we look at the slope for this perpendicular line, then we can find the slope of the line we are trying to find the equation for.
To find the slope of the perpendicular line given, we look to the coefficient of the $x$ term. For this line, the slope is $5$. Therefore, the negative reciprocal of $5$ is $-\frac{1}{5}$; this will be the slope of the line we are looking for.
Now that we have both the slope and y-intercept of the line, we can plug in those values into the slope-intercept formula:
$$y = -\frac{1}{5}x + 6$$
First, we subtract $2x$ from each side to get $y$ by itself:
$$y = -\frac{1}{5}x + 6$$
