find the slope of a line parallel to the line whose equation is $2x + 4y = 56$. fully simplify your answer.

Explanation:

Step1: Rewrite in slope - intercept form

The slope - intercept form is $y = mx + b$, where $m$ is the slope. Given $2x + 4y=56$, solve for $y$. First, subtract $2x$ from both sides: $4y=-2x + 56$.

Step2: Isolate $y$

Divide each term by 4: $y=-\frac{2}{4}x+\frac{56}{4}$, which simplifies to $y =-\frac{1}{2}x + 14$.

Step3: Determine the slope of the parallel line

Parallel lines have the same slope. The slope of the given line is $-\frac{1}{2}$, so the slope of a line parallel to it is also $-\frac{1}{2}$.

Answer:

$-\frac{1}{2}$