Question

What is an equation of the line that passes through the point (−1,−6) and is perpendicular to the line x+6y=6?

Answer 1

$\text{Hello!}$

$\boxed{y = 6x}$

$\text{Given equation:}\\x + 6y = 6\\\\\text{Rewrite the equation in the form y = mx + b to find the slope:}\\\\x + 6y = 6\\\\6y = -x + 6\\\\\\\text{Divide all terms by 6:}\\y = -x/6 + 1\\\\\text{Remember that a perpendicular line contains aslope of the negative reciprocal, therefore:}\\\\-1/6x \text{ becomes } 6\\\\\text{Use the coordinates given to find the equation of the perpendicular line:}\\\\(-6) = 6(-1) + b\\\\\\-6 = -6 + b\\\\b = 0\\\\\text{Therefore, the equation is:}$

$\boxed{y = 6x}$