Find the slope of a line perpendicular to the line whose equation is 6x +5y=-30. fully simplify your answer
To find the slope of a line perpendicular to the given line, we first need to find the slope of the given line. The equation of the given line is in the standard form \( \text{Ax + By = C} \), where A = 6, B = 5.
To find the slope of the line, we need to solve for y in the given equation:
\[ 6x + 5y = -30 \]
\[ y = -\frac{6}{5}x - 6 \]
Therefore, the slope of the given line is -6/5.
The slope of a line perpendicular to the given line is the negative reciprocal of the slope of the given line.
Thus, the slope of the line perpendicular to the given line is:
\[ \frac{5}{6} \]
Therefore, the slope of a line perpendicular to the line 6x + 5y = -30 is 5/6.