Question

question
find the equation of a line parallel to $4x + 4y = -8$ that passes through the point $(-1,4)$.

answer
$\circ\\ y + 4 = x - 1$ $\circ\\ y - 4 = x + 1$ $\circ\\ y + 4 = -(x - 1)$ $\circ\\ y - 4 = -(x + 1)$

Explanation:

Step1: Find slope of given line

Rewrite \(4x + 4y = -8\) in slope - intercept form (\(y=mx + b\), where \(m\) is the slope).
Subtract \(4x\) from both sides: \(4y=-4x - 8\).
Divide by 4: \(y=-x - 2\). The slope \(m=-1\). Parallel lines have the same slope, so the new line has slope \(m = - 1\).

Step2: Use point - slope form

Point - slope form is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(-1,4)\) and \(m=-1\).
Substitute: \(y - 4=-1(x - (-1))\), which simplifies to \(y - 4=-(x + 1)\).

Answer:

\(y - 4=-(x + 1)\) (the option with this equation)