How do you write an equation in slope-intercept form for the line that satisfies each set of conditions? The line passes through (-9, -3), perpendicular to y=-5/3x-8

##3x-5y+12=0##

The two lines are perpendicular to each other, if the product of their slopes is ##-1##. Hence if of one line is given as ##a/b##, slope of line perpendicular to it is ##-b/a##.

As equation of one line is given in as ##y=-5/3x-8##, its slope is ##-5/3##.

Hence slope of line perpendicular to it is ##3/5##.

Now equation of line passing through ##(x_1,y_1)## and having slope ##m## is ##(y-y_1)=m(x-x_1)##

Hence, equation of a line passing through ##(-9,-3)## and having a slope ##3/5## is

##(y-(-3))=3/5(x-(-9))##

or ##5(y+3)=3(x+9)##

or ##5y+15=3x+27##

or ##3x-5y+12=0## graph{(3x-5y+12)(y+5x/3+8)=0 [-20, 20, -10, 10]}