Find the slope of a line perpendicular to the line whose equation is 3, x, minus, 2, y, equals, 63x−2y=6. Fully simplify your answer.
To find the slope of a line perpendicular to a given line, we first need to find the slope of the given line.
The given line is represented by the equation 3x - 2y = 6.
To find the slope of this line, we can rewrite the equation in slope-intercept form (y = mx + b), where m is the slope:
3x - 2y = 6
-2y = -3x + 6
y = (3/2)x - 3
From the equation above, we see that the slope of the given line is 3/2.
The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.
Therefore, the slope of a line perpendicular to the given line is -2/3.
Fully simplified answer: -2/3