Question

question what is an equation of the line that passes through the point (2, - 2) and is perpendicular to the line x - 5y = 20? answer attempt 1 out of 2

Explanation:

Step1: Rewrite given line in slope - intercept form

Rewrite $x - 5y=20$ as $y=\frac{1}{5}x - 4$. The slope of this line is $m_1=\frac{1}{5}$.

Step2: Find slope of perpendicular line

The slope of a line perpendicular to a line with slope $m_1$ is $m_2=- \frac{1}{m_1}$. So, $m_2=-5$.

Step3: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Given the point $(2,-2)$ and $m=-5$, we have $y+2=-5(x - 2)$.

Step4: Expand and simplify

$y+2=-5x + 10$, which simplifies to $5x+y=8$.

Answer:

$5x + y=8$