Question
What line is parallel to y = 3/4 x - 2
Answers
GPT-4o mini
A line that is parallel to another line will have the same slope. The line you provided is in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
In your equation, \(y = \frac{3}{4}x - 2\), the slope \(m\) is \(\frac{3}{4}\).
Any line that is parallel to this will also have a slope of \(\frac{3}{4}\). You can write the equation of a parallel line in slope-intercept form as:
\[
y = \frac{3}{4}x + b
\]
where \(b\) can be any value. For example:
- If \(b = 0\), the parallel line is \(y = \frac{3}{4}x\).
- If \(b = 1\), the parallel line is \(y = \frac{3}{4}x + 1\).
- If \(b = -3\), the parallel line is \(y = \frac{3}{4}x - 3\).
You can choose any value for \(b\) to describe a specific line that is parallel to the given line.
In your equation, \(y = \frac{3}{4}x - 2\), the slope \(m\) is \(\frac{3}{4}\).
Any line that is parallel to this will also have a slope of \(\frac{3}{4}\). You can write the equation of a parallel line in slope-intercept form as:
\[
y = \frac{3}{4}x + b
\]
where \(b\) can be any value. For example:
- If \(b = 0\), the parallel line is \(y = \frac{3}{4}x\).
- If \(b = 1\), the parallel line is \(y = \frac{3}{4}x + 1\).
- If \(b = -3\), the parallel line is \(y = \frac{3}{4}x - 3\).
You can choose any value for \(b\) to describe a specific line that is parallel to the given line.