Find slope-intercept form of the equation of the line perpendicular to 2x+3y=24 and passing throug (-6,2)

Standard Form of Equation of the line: y=mx+b

we have 2x+3y=24

3y=24-2x

y=(-2/3)x + 24/3

y=(-2/3)x + 8

so m = -2/3 and b = 8

Since lines are perpendicular multiplicatin of their slope will be (-1)

So slope of the required line will be 3/2

Now we have a point (-6,2) and slope 3/2 of the line we can easily find required lines by putting these values in the equation of the straight line poin-slope form.

y=mx+b we have y=2 , x=-6 and m=3/2 find b

2=(3/2)*(-6) + b

2=-9+b

b=2+9

b=11

so slope-intercept form of the equation is y = (3/2)x + 11