The slope-intercept form of a line is: y = mx + b, where m represents the slope and b represents the y-intercept.
For the line y = 2/3x - 4, the slope is 2/3.
Any line perpendicular to that line has a slope that is the negative reciprocal of that slope.
The negative reciprocal of 2/3 is -3/2.
To find the new equation, start with y = mx + b.
Its slope is -3/2 and because it passes through the point (-5, 6) one of its x-values is -5 and one of its y-values is 6. Place these values into y = mx + b:
6 = (-3/2)(-5) + b
Now, solve for b: 6 = 15/2 + b ---> 6 = 7.5 + b --> b = -1.5
Place m = -3/2 and b = -1.5 into the slope-intercept form to get: y = -3/2x + -1.5
Simplifying: y = -1.5x - 1.5