Question

find the slope of a line parallel to the line whose equation is 6x + 3y = -54. fully simplify your answer. answer attempt 1 out of 2

Explanation:

Step1: Rewrite the equation in slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We start with the equation \(6x+3y=-54\).
First, we isolate \(y\). Subtract \(6x\) from both sides of the equation: \(3y=-6x - 54\).
Then, divide each term in the equation by 3: \(y=\frac{-6x}{3}-\frac{54}{3}\).
Simplify the fractions: \(y=-2x - 18\).

Step2: Determine the slope of the parallel line

Parallel lines have the same slope. In the equation \(y = - 2x-18\), the slope \(m\) of the given line is \(-2\). So, the slope of a line parallel to this line will also be \(-2\).

Answer:

\(-2\)