Question

geometry
name
unit 2 quiz
date
find the slope of a line parallel to each given line.

1. ( y = -x - 1 )
2. ( y = -6x - 1 )
3. ( y = -\frac{1}{3}x + 4 )

Explanation:

Step1: Recall the 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.

Step2: Use the property of parallel lines

Parallel lines have the same slope.

For \(y=-x - 1\)

In the equation \(y=-x - 1\), comparing with \(y = mx + b\), we have \(m=-1\). So the slope of a line parallel to \(y=-x - 1\) is \(-1\).

For \(y=-6x - 1\)

In the equation \(y=-6x - 1\), comparing with \(y = mx + b\), we have \(m=-6\). So the slope of a line parallel to \(y=-6x - 1\) is \(-6\).

For \(y =-\frac{1}{3}x+4\)

In the equation \(y =-\frac{1}{3}x + 4\), comparing with \(y=mx + b\), we have \(m =-\frac{1}{3}\). So the slope of a line parallel to \(y =-\frac{1}{3}x + 4\) is \(-\frac{1}{3}\).

Answer:

1. \(-1\)
2. \(-6\)
3. \(-\frac{1}{3}\)