The equation in the problem in written in slope-intercept form (i.e. y= mx + b) where the slope (m) is 4/3 and the y-intercept (b) is 6.
When lines are perpendicular, their slopes are negative reciprocals. So the slope of the line perpendicular to the one in the problem is -3/4.
The new equation for the perpendicular line will be: y = -3/4x + b
We can use the given point to determine the y-intercept for the perpendicular line by substituting x as -4 and y as -1 and solving for the y-intercept b.
y = -3/4 x + b
-1 = (-3/4)*(-4) + b
-1= 3 + b
-1 -3 = 3 + b - 3
-4 = b
So the equation of the perpendicular line is: y = -3/4 x - 4
