Write an equation in point-slope form for the line through the given point with the given slope.(4, –6); m=3/5

Using:

y - y₁= m(x - x₁)

m = slope = 3/5,  (x₁, y₁) = (4, -6)      x₁ = 4, y₁ = -6

y - y₁= m(x - x₁)

y - (-6) = (3/5)(x - 4)

y + 6 =(3/5)(x - 4)

5*(y + 6) = 3*(x - 4)

5y + 30 = 3x - 12

5y = 3x - 12 - 30

5y = 3x - 42

So equation of line is   5y = 3x - 42