Question

find the equation of a line perpendicular to -5x + y = -2 that passes through the point (5,4).
answer
y = -\frac{1}{5}x + 5 -5x + y = -21
x - 5y = -15 y = \frac{1}{5}x + 5

Explanation:

Step1: Rewrite the given line in slope - intercept form

Rewrite $-5x + y=-2$ as $y = 5x - 2$. The slope of this line is $m_1 = 5$.

Step2: Find the slope of the perpendicular line

If two lines are perpendicular, the product of their slopes is $- 1$. Let the slope of the perpendicular line be $m_2$. Then $m_1\times m_2=-1$. Since $m_1 = 5$, we have $5\times m_2=-1$, so $m_2=-\frac{1}{5}$.

Step3: Use the point - slope form to find the equation of the line

The point - slope form is $y - y_1=m_2(x - x_1)$, where $(x_1,y_1)=(5,4)$ and $m_2=-\frac{1}{5}$. Substitute these values: $y - 4=-\frac{1}{5}(x - 5)$.

Step4: Simplify the equation

Expand the right - hand side: $y - 4=-\frac{1}{5}x+1$. Add 4 to both sides to get $y=-\frac{1}{5}x + 5$.

Answer:

$y =-\frac{1}{5}x + 5$