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) reset next

Explanation:

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

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

Step2: Find perpendicular slope

Perpendicular slope is negative reciprocal: $m=\frac{6}{5}$

Step3: Solve for y-intercept $b$

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

Step4: Write line equation

Substitute $m$ and $b$ into $y=mx+b$

Answer:

$y=\frac{6}{5}x+\frac{8}{5}$
(The first box is $\frac{6}{5}$, the second box is $\frac{8}{5}$)