Which equation passes through this point (2,5) and is perpendicular to 3y = 12x – 9?

Question

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Answer 1

3y=12x-9 is the same as

y=4x-3 (just divide both sides by 3) the slope =4, the coefficient of the x term

the line perpendicular to it has slope = the negative inverse of 4, or -1/4

y=-x/4 + b. Plug in the point to find b

5=-2/4 + b

20=-2 + 4b

4b = 22

b = 22/4 = 11/2

y=-x/4 + 11/2 eliminate the fractions by multiplying by 4

4y =-x +22

x+4y = 22 is the equation for the perpendicular line through the point (2,5)