The straight line l_2 is perpendicular to l_1 with equation y = \frac{2}{3}x - 2 and passes through Q (5, −3).

Find an equation for l_2 in the form ax + by = c, where a, b and c are integer constants.
Find an equation for l_2 in the form ax + by = c, where a, b and c are integer constants.
Step 1: Calculate the slope of the given line equation
NOTE: Putting the equation in the form y = mx (+c) and attempting to
extract the m
Step 2: Find the slope of the another line
NOTE: i) Parallel lines have the same slope.
ii) Perpendicular lines have slopes that are opposite reciprocals, like
\frac{a}{b} \text{ and } \frac{-b}{a} The slopes also have
a product of -1.
Step 3: Use the slope of line and a point on line to find its y-intercept.
EXAMPLE: Plug the slope m = -2 and the point (-6, 4) into the
slope- intercept formula. Then solve for the y-intercept b.
y = mx + b
4 = -2(-6) + b
Step 4: Use the slope of line and the y-intercept of line to find the equation of the line.
EXAMPLE: Plug the slope m = -2 and the y-intercept b = -8 into the
slope- intercept formula.
y = mx + b
y = -2x + -8