Question

find the slope of a line parallel to the line whose equation is 6x + 3y = -54. fully simplify your answer.

Explanation:

Step1: Rewrite the equation in slope - intercept form

The slope - intercept form is $y = mx + b$, where $m$ is the slope. Start with $6x + 3y=-54$. Isolate $y$:
$3y=-6x - 54$.

Step2: Solve for $y$

Divide each term by 3: $y=\frac{-6x}{3}-\frac{54}{3}$, so $y=-2x - 18$.

Step3: Identify the slope

The slope of the line $y=-2x - 18$ is $m=-2$.

Step4: Recall the property of parallel lines

Parallel lines have the same slope. So the slope of a line parallel to the given line is also $-2$.

Answer:

$-2$