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

1 answer

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:

\[ 2y = -5x + 6 \]

  1. 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

\[ -\frac{5}{2}. \]