# How do you write an equation of a line passing through (1, -1), perpendicular to  y=3x+2?

$y + 1 = - \frac{1}{3} \cdot \left(x - 1\right)$ or $y = - \frac{1}{3} x - \frac{2}{3}$
If a line is perpendicular to another this means its slope is the opposite reciprocal of the other function's slope. Opposite meaning the sign switches and reciprocal meaning one over the number. In this case the slope of this function is 3 and its opposite reciprocal is $- \frac{1}{3}$ which means we now know the slope of the perpendicular line.
We also know one point which must be on the line so we can plug this into the point-slope formula ($y - y 1 = m \left(x - x 1\right)$ where y1 is the y-coordinate of a point on the line, x1 is the corresponding x-coordinate, and m is the slope) to get $y - \left(- 1\right) = - \frac{1}{3} \cdot \left(x - 1\right)$. Which should be a perfectly valid answer, but if you meed it in slope-intercept form just subtract one from both sides to solve for y. This will give you $y = - \frac{1}{3} x - \frac{2}{3}$. Hope I helped!