Answer:
- y = (-1/6)x +4/3
- y = x -2
- y = -2x +6
Step-by-step explanation:
A simple, mechanical way to do these (perpendicular lines) is ...
- replace any constant with 0
- swap the x- and y-coefficients, negating one
- for point (h, k), replace x with (x-h) and y with (y-k)
- solve for y (to get slope-intercept form)
1) (x+4) +6(y -2) = 0 . . . .after step 3 above
... x -8 = -6y . . . . . . . . . . eliminate parentheses, add the opposite of the y-term
... y = (-1/6)x +4/3 . . . . . divide by the y-coefficient
2) (y+5) = (x +3)
... y = x -2 . . . . . . . . . . . . . add -5
3) (1/2)(y -4) = -(x -1)
... 1/2y -2 = -x +1 . . . . . . . eliminate parentheses
... 1/2y = -x +3 . . . . . . . . . add 2
... y = -2x +6 . . . . . . . . . . . multiply by 2
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Comment on the graph(s)
The attached graphs show the original lines and points (1: red, 2: blue, 3: green). The original line is dashed, and the perpendicular line through the point is shown solid. This confirms the results above.
