The equations of the lines are:
1) y - 5 = (1/3)(x - 12)
2) y + 8 = -4x
Let's find the equations:
To find the equation in point-slope form of the line with slope 1/3 and passing through (12, 5):
Point-slope form: y - y₁ = m(x - x₁)
Plug in the known values: y - 5 = (1/3)(x - 12)
For the line with slope -4 and passing through (0, -8):
Use the same point-slope form: y - (-8) = (-4)(x - 0)
Simplify: y + 8 = -4x
The equation in point-slope form for the second line is y + 8 = -4x.