Question

write the equation of a line through of (-1,-5), perpendicular to $y = \frac{1}{9}x + 5$
$y = \square x + \square$

Explanation:

Step1: Find perpendicular slope

The slope of $y=\frac{1}{9}x+5$ is $\frac{1}{9}$. Perpendicular slope $m = -9$ (negative reciprocal).

Step2: Substitute point into slope-intercept form

Use point $(-1,-5)$ and $y=mx+b$:
$-5 = -9(-1) + b$
$-5 = 9 + b$

Step3: Solve for y-intercept b

$b = -5 - 9 = -14$

Step4: Write final line equation

Substitute $m=-9$ and $b=-14$ into $y=mx+b$.

Answer:

$y = -9x + (-14)$ or simplified as $y = -9x - 14$