Question

Find the equation for the line that passes through the point (-2,-1) that is perpendicular to the line which the equation y=2/3x-5

Answer 1

In order to find the required line equation, first consider that the realtion between slopes of perpendicular lines is given by:

$m_1=-\frac{1}{m_2}$

In this case, one of the slopes is m2 = 2/3, then, the slope of the perpendicular line:

$m_1=-\frac{1}{\frac{2}{3}}=-\frac{3}{2}$

Now, use the following general equation for a line:

$y-y_o=m_1(x-x_o)$

where (xo , yo) = (-2 , -1). Replace the values of m1, xo and yo into the previous equation and solve for y, as follow:

$\begin{gathered} y-(-1)=-\frac{3}{2}(x-(-2)) \\ y+1=-\frac{3}{2}x-3 \\ y=-\frac{3}{2}x-3-1 \\ y=-\frac{3}{2}x-4 \end{gathered}$

Hence, the equation for the perpendicular line is:

y = -3/2 x - 4