Barrett and Penelope have some quarters for the vending machine.
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It can be handy to start with a version of the point-slope form of the equation for a line. For a line of slope m through point (h, k), an equation can be written as
... y = m(x -h) +k
The given line can be solved for y to get
... y = (3x -6)/2
Then the slope is the x-coefficient, 3/2.
The parallel line through (2/5, -1) will have the same slope, so its equation can be written
... y = (3/2)(x -2/5) -1
... y = (3/2)x -8/5 . . . . parallel line
The perpendicular line will have a slope that is the negative reciprocal of 3/2, that is, -2/3. Its equation can be written as
... y = (-2/3)(x -2/5) -1
... y = (-2/3)x -11/15 . . . . perpendicular line
