Question

find the equation of a line perpendicular to 4x + y = -8 that passes through the point (-8,5).
answer
y = -4x - 8
y = -\frac{1}{4}x + 7
y = 4x - 8
y = \frac{1}{4}x + 7

Explanation:

Step1: Rewrite the given line in slope - intercept form

Rewrite $4x + y=-8$ as $y=-4x - 8$. The slope of this line is $m_1=-4$.

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 $m_1\times m_2=-1$. Substituting $m_1 = - 4$ gives $-4m_2=-1$, so $m_2=\frac{1}{4}$.

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 $(x_1,y_1)=(-8,5)$ and $m_2=\frac{1}{4}$. Substitute these values: $y - 5=\frac{1}{4}(x + 8)$.

Step4: Simplify the equation

Expand the right - hand side: $y-5=\frac{1}{4}x + 2$. Then add 5 to both sides to get $y=\frac{1}{4}x+7$.

Answer:

$y=\frac{1}{4}x + 7$