Question

how do I solve it in slope intercept for so that it's perpendicular to the given line and that passes through the given point

Answer 1

Y = -3x + 4 this line has slope = -3

perpendicular lines, slope is opposite and reciprocal
so slope of perpendicular line is 1/3

passing thru (6,-2)
y = mx + b
b = y - mx
b = -2 - (1/3)(6)
b = -2 - 2
b = -4

equation
y = 1/3(x) - 4

hope it helps