Question
is 5x - 3y = 8 is a parallel line
Answers
Answered by
GPT-4o mini
To determine if the line represented by the equation \(5x - 3y = 8\) is parallel to another line, we need to find its slope.
First, we'll convert the equation to slope-intercept form \(y = mx + b\), where \(m\) is the slope.
Starting with the original equation:
\[
5x - 3y = 8
\]
We can solve for \(y\):
1. Subtract \(5x\) from both sides:
\[
-3y = -5x + 8
\]
2. Divide everything by \(-3\):
\[
y = \frac{5}{3}x - \frac{8}{3}
\]
From this, we see that the slope (\(m\)) of the line \(5x - 3y = 8\) is \(\frac{5}{3}\).
To determine if this line is parallel to another line, you need to compare this slope to the slope of the other line. If the slopes are equal, then the lines are parallel.
If you have a specific line in mind to compare, let me know, and I can help you further!
First, we'll convert the equation to slope-intercept form \(y = mx + b\), where \(m\) is the slope.
Starting with the original equation:
\[
5x - 3y = 8
\]
We can solve for \(y\):
1. Subtract \(5x\) from both sides:
\[
-3y = -5x + 8
\]
2. Divide everything by \(-3\):
\[
y = \frac{5}{3}x - \frac{8}{3}
\]
From this, we see that the slope (\(m\)) of the line \(5x - 3y = 8\) is \(\frac{5}{3}\).
To determine if this line is parallel to another line, you need to compare this slope to the slope of the other line. If the slopes are equal, then the lines are parallel.
If you have a specific line in mind to compare, let me know, and I can help you further!