Question

Write the equation of a line that is perpendicular to the given line and that passes through the given point. y=2/3x+9; (-6,5)

A: y=-2/3x+1
B: y=-3/2x-4
C: y=-3/2x+3/2
D: y=2/3+9

Answer 1

perpendicular lines are always the negative (opposite) reciprocal of the current line's slope:

\(\large \frac{2}{3}\) is now \(\large -\frac{3}{2}\)

now substitute the x- and y-values and the slope of the perpendicular line into the slope-intercept formula:

\(\large y= mx + b\)
\(\large 5 = -\frac{3}{2}(-6) + b\)

solve for \(\large b\)