Find the slope of a line perpendicular to the line whose equation is 4, x, minus, 6, y, equals, minus, 244x−6y=−24. Fully simplify your answer.
To find the slope of the line 4x - 6y = -24, we need to rearrange the equation into slope-intercept form, y = mx + b, where m is the slope.
4x - 6y = -24
-6y = -4x - 24
y = (2/3)x + 4
The slope of this line is m = 2/3.
The slope of a line perpendicular to this line can be found by taking the negative reciprocal of the slope.
The negative reciprocal of 2/3 is -3/2.
Therefore, the slope of the line perpendicular to 4x - 6y = -24 is -3/2.