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Find an equation of the line through (-1,4) and perpendicular to 2x+3y=8

Hello:

2x+3y=8

y = (-2/3) x+8/3 (the slope is : (-2/3))

an equation of the line through (-1,4) and perpendicular to 2x+3y=8

is : y = ax+b

the slope is a : a * (-2/3) = - 1 ... (perpendicular to a line with a slope of - 2/3)

a = 3/2 y = (3/2) x+b

the line that passes through (-1, 4) : 4 = (3/2) (-1) + b

b = 11/2

the equation is : y = (3/2) x+11/2