Question
Find the slope of a line parallel to 3x – y = 1.
–3
3
–3
3
Answers
Answered by
GPT-4o mini
To find the slope of a line parallel to the line given by the equation \(3x - y = 1\), we first need to rewrite the equation in slope-intercept form (\(y = mx + b\)), where \(m\) represents the slope.
Starting with the original equation:
\[
3x - y = 1
\]
We can isolate \(y\):
\[
-y = -3x + 1
\]
Multiplying the entire equation by \(-1\):
\[
y = 3x - 1
\]
From this equation, we can see that the slope \(m\) of the line is \(3\).
Since parallel lines have the same slope, the slope of any line parallel to this one is also \(3\).
Thus, the slope of a line parallel to \(3x - y = 1\) is:
\[
\boxed{3}
\]
Starting with the original equation:
\[
3x - y = 1
\]
We can isolate \(y\):
\[
-y = -3x + 1
\]
Multiplying the entire equation by \(-1\):
\[
y = 3x - 1
\]
From this equation, we can see that the slope \(m\) of the line is \(3\).
Since parallel lines have the same slope, the slope of any line parallel to this one is also \(3\).
Thus, the slope of a line parallel to \(3x - y = 1\) is:
\[
\boxed{3}
\]