Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).
triangle abc is defined by the points a(2,9), b(8,4), and c(-3,-2).
complete the following equation for a line passing through point c and perpendicular (overline{ab}).
( y = square x + square )

Explanation:

Step1: Calculate slope of $\overline{AB}$

Slope formula: $m_{AB} = \frac{y_2-y_1}{x_2-x_1} = \frac{4-9}{8-2} = -\frac{5}{6}$

Step2: Find perpendicular slope

Perpendicular slope $m = \frac{6}{5}$ (negative reciprocal)

Step3: Solve for y-intercept

Use point $C(-3,-2)$: $-2 = \frac{6}{5}(-3) + b$
$-2 = -\frac{18}{5} + b$
$b = -2 +\frac{18}{5} = \frac{-10 +18}{5} = \frac{8}{5}$

Answer:

$y=\frac{6}{5}x+\frac{8}{5}$