Line through a point in quadrant 3 perpendicular to another line: Find the general equation of the line through (-1,-3) and perpendicular to 2x + y - 4 = 0.

We need the slope of the given line. Solve for the slope-intercept form:

y = -2x + 4, or the slope is -2.

Consequently, the perpendicular line has a slope .

We can now use this slope in the point-slope form to find the equation of the desired line:

, or , or

We can check that this line goes through the given point by substituting the coordinates (-1,-3) in the equation:

and the point is on the line as required.

Test Problem: Find the general equation of the line through (-4,-2) and
perpendicular to x - 3y - 9 = 0.

a) x + 3y + 2 = 0

b) 3x - y + 10 = 0

c) 3x + y + 14 = 0

d) 3x + y + 10 = 0

e) x - 3y - 2 = 0