Question

what is the equation of a line that passes through (-2,-3) and is perpendicular to 2x-3y=6

Answer 1

Find the slope of \(2x-3y=6\). Any line perpendicular to this one will have a negative reciprocal slope, meaning if the slope of the first line is \(\dfrac{a}{b}\), then the slope of the perpendicular line is \(-\dfrac{b}{a}\).

Then, use the point-slope formula:
\[y-y_0=m(x-x_0)\]
where \((x_0,y_0)\) is the given point, \((-2,-3)\), and \(m\) is the slope of the perpendicular.