Question

4.
Find the slope of a line parallel to 5x + 2y = 6

Answer 1

To find the slope of a line parallel to the given line \(5x + 2y = 6\), we first need to determine the slope of the original line.

1. Start by rewriting the equation in slope-intercept form (y = mx + b), where \(m\) is the slope.

Begin with the original equation:
\[
5x + 2y = 6
\]

2. Solve for \(y\):
\[
2y = -5x + 6
\]
\[
y = -\frac{5}{2}x + 3
\]

3. From the equation \(y = -\frac{5}{2}x + 3\), we see that the slope \(m\) of the line is \(-\frac{5}{2}\).

Since parallel lines have the same slope, the slope of a line parallel to the given line is also \(-\frac{5}{2}\).

Thus, the slope of a line parallel to \(5x + 2y = 6\) is \(\boxed{-\frac{5}{2}}\).