Question

Write the slope intercept forms of the equations of the lines through the given point that is a) parallel to the given line and b) perpendicular to the given line: (2/5,-1), 3x -2y=6

Answer 1

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