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11Alexandr11 [23.1K]
2 years ago
10

Determine the equation of a line through the point (3,-4) that is perpendicular to the line y=3x+7

Mathematics
1 answer:
Lana71 [14]2 years ago
7 0

Answer:

y = - \frac{1}{3} x - 3

Step-by-step explanation:

The equation of a line in slope- intercept fprm is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 7 is in slope- intercept form

with slope m = 3

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

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{3}, thus

y = - \frac{1}{3} x + c ← is the partial equation of the perpendicular line

To find c substitute (3, - 4) into the partial equation

- 4 = - 1 + c ⇒ c = - 4 + 1 = - 3

y = - \frac{1}{3} x - 3 ← equation of perpendicular line

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D. 4.75, 12.25, 16.25, side lengths can form a triangle.

Step-by-step explanation:

We are given three sides in options A, B , C and D.

We need to check if the given sides would form a triangle or not.

Note: Sum of two sides is always greater than third sides in a triangle.

So, we need to check the sum of two sides of given sides length to check if sum is greater than third side length.

A. 5,8,12.

5+8 is greater than 12.

5+12 is greater than 8.

12+8 is greater than 5.

Therefore A. 5,8,12, side lengths can form a triangle.

B. 20, 18, 2

18+2 is not greater than 20.

Therefore B. 20, 18, 2, side lengths can not form a triangle.

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15+9 is less than 26.

Therefore C. 15, 26 , 9, side lengths can not form a triangle.

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4.75+12.25 is greater than 16.25.

4.75+16.25 is greater than 12.25.

12.25+16.25 is greater than 4.75.

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