Question

2 multiple choice 1 point are the following lines parallel, perpendicular, or neither? $y = \frac{4}{7}x + 1$ $y = \frac{4}{7}x - 1$ parallel perpendicular neither clear my selection

Explanation:

Step1: Recall the slope-intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope of the line and \(b\) is the y - intercept.

Step2: Find the slopes of the two lines

For the line \(y=\frac{4}{7}x + 1\), by comparing with \(y=mx + b\), we can see that the slope \(m_1=\frac{4}{7}\).
For the line \(y=\frac{4}{7}x-1\), by comparing with \(y = mx + b\), we can see that the slope \(m_2=\frac{4}{7}\).

Step3: Determine the relationship between the lines

Two lines are parallel if their slopes are equal (\(m_1=m_2\)) and they have different y - intercepts (to ensure they are not the same line). Here, \(m_1 = m_2=\frac{4}{7}\) and the y - intercepts are \(1\) and \(- 1\) (which are different). So the two lines are parallel.

Answer:

A. Parallel