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Find the slope of a line parallel to 5x + 2y = 6Question
Find the slope of a line parallel to 5x + 2y = 6.
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Answered by
GPT-4o mini
To find the slope of a line parallel to the line given by the equation \(5x + 2y = 6\), we first need to express this equation in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope.
Starting with the original equation:
\[
5x + 2y = 6
\]
we isolate \(y\):
1. Subtract \(5x\) from both sides:
\[
2y = -5x + 6
\]
2. Now divide every term by \(2\):
\[
y = -\frac{5}{2}x + 3
\]
From this equation, the slope \(m\) is \(-\frac{5}{2}\).
Since parallel lines have the same slope, the slope of a line parallel to the line given by \(5x + 2y = 6\) is also
\[
-\frac{5}{2}.
\]
Starting with the original equation:
\[
5x + 2y = 6
\]
we isolate \(y\):
1. Subtract \(5x\) from both sides:
\[
2y = -5x + 6
\]
2. Now divide every term by \(2\):
\[
y = -\frac{5}{2}x + 3
\]
From this equation, the slope \(m\) is \(-\frac{5}{2}\).
Since parallel lines have the same slope, the slope of a line parallel to the line given by \(5x + 2y = 6\) is also
\[
-\frac{5}{2}.
\]