Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar.triangle abc is defined by the points a(3,8), b(7,5), and c(2,3).create an equation for a line passing through point a and perpendicular to $overline{bc}$.$y= \square x + \square$

Explanation:

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

Points $B(7,5)$ and $C(2,3)$. Slope formula: $m_{BC}=\frac{y_2-y_1}{x_2-x_1}=\frac{3-5}{2-7}=\frac{-2}{-5}=\frac{2}{5}$

Step2: Find perpendicular slope

Perpendicular slope is negative reciprocal: $m=-\frac{5}{2}$

Step3: Use point-slope form for line

Use point $A(3,8)$: $y-y_1=m(x-x_1)$
$y-8=-\frac{5}{2}(x-3)$

Step4: Convert to slope-intercept form

Expand and solve for $y$:
$y-8=-\frac{5}{2}x+\frac{15}{2}$
$y=-\frac{5}{2}x+\frac{15}{2}+8$
$y=-\frac{5}{2}x+\frac{15}{2}+\frac{16}{2}=-\frac{5}{2}x+\frac{31}{2}$

Answer:

$y=-\frac{5}{2}x+\frac{31}{2}$
(The first box is $-\frac{5}{2}$, the second box is $\frac{31}{2}$)