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Andreyy89
2 years ago
12

What is an equation of the line that passes through the point (1,-3) and is perpendicular to the line x+3y=21?

Mathematics
1 answer:
andreev551 [17]2 years ago
7 0

Answer:

3x - y = 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Given

x + 3y = 21 ( subtract x from both sides )

3y = - x + 21 ( divide all terms by 3 )

y = - \frac{1}{3} x + 7 ← in slope- intercept form

with slope m = - \frac{1}{3}

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

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

y = 3x + c ← is the partial equation

To find c , substitute (1, - 3) into the partial equation

- 3 = 3 + c ⇒ c = - 3 - 3 = - 6

y = 3x - 6 ← in slope- intercept form

subtract y from both sides

0 = 3x - y - 6 ( add 6 to both sides )

6 = 3x - y , that is

3x - y = 6 ← in standard form

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From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh
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Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

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considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

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