Write the equation of a line that is perpendicular to the given line and that passes through the given point. y+2=1/3(x-5); (-4,3)

Can someone explain this?

canned answer is wrong again.

new slope = -3 , (they had that part correct)

new equation through (-4,3)
y - 3 = -3(x + 4)
y - 3 = -3x - 12
y = -3x - 9

The equation of a line that is perpendicular to the given line and that passes through the given point can be written as y = -3x + b, where b is the y-intercept. To find the value of b, we can substitute the given point into the equation:

3 = -3(-4) + b
b = 15

Therefore, the equation of the line is y = -3x + 15.