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which of these is a point slope equation of the line that is perpendicular to y - 8 = 3(x -10) and passes through -2, 7 A. y - 7 = -1/3 (x+2) B. y - 7 = -3 (x+2) C. y+7=-1/3(x-2) D. Y+7=3(x-2)

User Khanhlvg
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6.1k points

2 Answers

5 votes

Answer:

A

Explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 8 = 3(x - 10) is in this form

with slope m = 3

Given a line with slope m then the slope of a line perpendicular to it is


m_(perpendicular) = -
(1)/(m) = -
(1)/(3)

the line passes through (a, b) = (- 2, 7), hence

y - 7 = -
(1)/(3)(x - (- 2)), that is

y - 7 = -
(1)/(3)(x + 2) → A

User IReXes
by
5.4k points
7 votes

Answer: OPTION A

Explanation:

The form of point slope equation of the line is:


(y-y_1)=m(x-x_1)

Where m is the slope and (
x_1,y_1) is a poing of the line.

The line given is:


y-8=3(x-10)

So the slope of this line is m=3

By definition, if two lines are perpendicular to each other, then theis slopes are opposite reciprocals. Therefore the slope of the other line must be:


m=-(1)/(3)

Substituting the slope and the points given into the formula, you obtain that the line is:


(y-7)=-(1)/(3)(x+2)

User Meara
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6.8k points