write an equation of the line that passes through (1,-6) and is perpendicular to the line y=3x+7

Question

abb0t · Answer

The relationship for the slopes of perpendicular lines is: $m_1 \times m_2 = -1$
You already have $m_1$ but you don't have $m_2$ so solve for it. If you have $3m_2=-1$, what is $m_2$? 

Now, you can use the point-slope equation: $y - y_1 = m(x - x_1)$ which you should be familiar with. To get the new equation that's perpendicular to your first line.

abb0t · Answer

remember, perpendicular means $\perp$

abb0t · Answer

You could also use calculus to solve this. Simply find the derivative of your function y = mx+ b with respect to "x". 
Then, use the inverse of the slope (to get your perpendicular). Then follow the same steps, plug in your new slope into your point-slope equation solvinf rot the new equation. Good Luck. Cheers