Question 174054
First, recall that if two lines are perpendicular to each other, then their slopes are the negative reciprocal of each other. In other words, if you were to multiply the slopes of two perpendicular lines, the result would be -1.
So first you need to find the slope of the line represented by the given equation: y = 3x+2.
Since this equation is already in the "slope-intercept" form: y = mx+b, you can see that its slope, m = 3, so the negative reciprocal of 3 is {{{-1/3}}} and this will be the slope of the new line. You can then start the equation of the new line with:
{{{y = (-1/3)x+b}}} Next, you need to find the value of b, the y-intercept.  You can do this by substituting the x- and y-coordinates of the given point (1, -1) into the equation above:
{{{-1 = (-1/3)(1) + b}}} Now you can solve this for the value of b. Add {{{(1/3)}}} to both sides.
{{{-1+(1/3) = b}}} Simplify the left side.
{{{b = -2/3}}} Now you can write the final equation for the new line.
{{{highlight(y = (-1/3)x-2/3)}}}