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