Write the equation of a line perpendicular to 3x-4y=-9 that passes through the point ​(-3​,3)

Answer 1

3x-4y = -9

4y = 3x + 9

y = 3x/4 + 9/4

slope = the coefficient of the x term, when the equation is solved for y. m=3/4

(-3,3)

a perpendicular line has a negative inverse slope

negative inverse of 3/4 is -4/3. just flip the fraction upside down and change the sign

y=mx + b

y= -4x/3 + b. to solve for b plug in the point (x,y)= (-3,3)

3 = -4(-3)/3 + b

3 = 4 +b

b = 3-4 = -1

b =-1

y =-4x/3 -1 is the equation of the perpendicular line through the given point