Question

consider the line 6x - 3y = 6.
what is the slope of a line parallel to this line?
what is the slope of a line perpendicular to this line?
slope of a parallel line:
slope of a perpendicular line:

Explanation:

Step1: Convert to slope - intercept form

We start with the equation \(6x - 3y=6\). We want to solve for \(y\) to get it in the form \(y = mx + b\), where \(m\) is the slope.
Subtract \(6x\) from both sides: \(- 3y=-6x + 6\).
Then divide each term by \(-3\): \(y=\frac{-6x}{-3}+\frac{6}{-3}\), which simplifies to \(y = 2x-2\). So the slope \(m\) of the given line is \(2\).

Step2: Find slope of parallel line

Parallel lines have the same slope. So the slope of a line parallel to the given line is also \(2\).

Step3: Find slope of perpendicular line

The slope of a line perpendicular to a line with slope \(m\) is the negative reciprocal of \(m\). If \(m = 2\), the negative reciprocal is \(-\frac{1}{2}\).

Answer:

Slope of a parallel line: \(2\)
Slope of a perpendicular line: \(-\frac{1}{2}\)