Find the slope of a line perpendicular to the line whose equation is 3x-2y=14. Fully simplify your answer.
To find the slope of the line perpendicular to 3x - 2y = 14, we first need to determine the slope of the given line.
Rearranging the equation into slope-intercept form (y = mx + b), we get:
2y = 3x - 14
y = (3/2)x - 7
The slope of the given line is 3/2.
To find the slope of a line perpendicular to this line, we take the negative reciprocal of 3/2:
Perpendicular slope = -2/3
Therefore, the slope of a line perpendicular to 3x - 2y = 14 is -2/3.