Question

find the equation of the line that is perpendicular to y = 6x - 2 and contains the point (6,-2). y = -\frac{?}{\square}x + \square

Explanation:

Step1: Find perpendicular slope

The slope of $y=6x-2$ is $6$. Perpendicular slope is negative reciprocal: $m = -\frac{1}{6}$

Step2: Substitute point into slope-intercept form

Use point $(6,-2)$ and $y = mx + b$:
$-2 = -\frac{1}{6}(6) + b$

Step3: Solve for y-intercept b

Simplify and solve:
$-2 = -1 + b$
$b = -2 + 1 = -1$

Answer:

$y = -\frac{1}{6}x - 1$
(The missing numerator is 1, denominator is 6, and the constant term is -1)