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Answer 1

Perpendicular lines have negative reciprocal slopes (in which the product of those two slopes = -1). The negative reciprocal of 1/3 is -3.

Therefore, the following choices are perpendicular to y — 1 = 1/3(x + 2):


You’ll have to transform option 1 into its slope-intercept form to see whether its slope is a negative reciprocal to 1/3:

OPTION 1:

y + 2 = -3(x - 4)
Distribute -3 into the parenthesis, and subtract 2 from both sides:
y + 2 - 2 = -3x + 12 - 2
y = -3x + 10

OPTION 5:
You’ll also have to transform option 5 into its slope-intercept form:

3x + y = 7
Subtract 3x from both sides to isolate y:
3x - 3x + y = - 3x + 7
y = -3x + 7


OPTION 3:
Option 3 also has a negative reciprocal slope of -3:

y = -3x - 5/3

Therefore, the following options are the correct answers:

Option 1: y + 2 = -3(x —4)
Option 3: y = -3x - Five-thirds or y = -3x - 5/3
Option 5: 3x + y = 7


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