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statuscvo [17]
3 years ago
9

Write the slope intercept equation of a line which is parallel to y=3x+5 passing through (-6,3). Can anyone please explain with

the formula?

Mathematics
2 answers:
Eduardwww [97]3 years ago
5 0

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

If lines are parallel then they have the same slope (m)

This means that the slope of the line will be 3 :

y = 3x + b

Now we must find b

To do that you must plug in the point the line goes through in the x and y of the equation.

(-6, 3)

3 = 3(-6) + b

3 = -18 + b

21 = b

y = 3x + 21

Hope this helped!

~Just a girl in love with Shawn Mendes

Studentka2010 [4]3 years ago
5 0

Answer:

y = 3x + 21

Step-by-step explanation:

The formula of a line goes in y= mx + c

Parallel lines have different y-intercepts but the same gradients so we can assume that

y = 3x + c

Substitute in the coordinates (-6 , 3) to work out the full equation

3 = -18 + c

So c = 21

Therefore the equation of the line that is parallel to y=3x+5 passing through (-6,3) is y = 3x + 21

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Let ƒ(x) = x + 1 and g(x) = 5x. Evaluate the composition (ƒ ∘ g)(–1). Question 2 options: A) (ƒ ∘ g)(–1) = 6 B) (ƒ ∘ g)(–1) = –4
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5 0
3 years ago
A fence must be built to enclose a rectangular area of 20,000 ft^2. Fencing material costs $4 per foot for the two sides facing
Marysya12 [62]

The cost of the least expensive fence is $3200

Step-by-step explanation:

The given is:

  • A fence must be built to enclose a rectangular area of 20,000 ft²
  • Fencing material costs $4 per foot for the two sides facing north and south and ​$8 per foot for the other two sides

We need to find the cost of the least expensive fence

Assume that the length of each side opposite to North or South is x feet and the length of each other sides  is y feet

∵ The length of the rectangle = x feet

∵ The width of the rectangle = y feet

∵ The rectangular area is 20,000 ft²

- Area of a rectangle = length × width

∴ x × y = 20,000

- Divide both sides by x to find y in terms of x

∴ y=\frac{20,000}{x}

The fence's length is equal to the perimeter of the rectangular area

∵ Perimeter of the rectangle = 2 length + 2 width

∴ Perimeter of the rectangle = 2x + 2y

∵ Fencing material costs $4 per foot for the two sides facing

   North and South

∴ x costs $4 per foot

∵ The cost of the other two sides is $8 per foot

∴ y costs $8 per feet

The cost of the fence is the sum of the products of 4 , 2x and 8 , 2y

∵ The cost of the fence (C) = 4(2x) + 8(2y)

∴ C = 8x + 16y

- Substitute y by its value above

∴ C=8x+16(\frac{20,000}{x})

∴ C=8x+\frac{320,000}{x}

To find the least expensive differentiate C with respect to x and equate the answer by 0 to find the value of x

∵ \frac{320,000}{x} can be written as 320,000x^{-1}

∴ C=8x+320,000x^{-1}

∵ \frac{dC}{dx}=8(1)x^{1-1}+320,000(-1)x^{-1-1}

∴ \frac{dC}{dx}=8-320,000x^{-2}

- Equate \frac{dC}{dx} by zero

∴ 8-320,000x^{-2}=0

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∴ 8-\frac{320,000}{x^{2}}=0

- Subtract 8 from both sides

∴ -\frac{320,000}{x^{2}}=-8

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∴ - 320,000 = - 8x²

- Divide both sides by -8

∴ 40,000 = x²

- Take √  for both sides

∴ 200 = x

Substitute x in the equation of C to find the least cost of fence

∵ C=8(200)+\frac{320,000}{(200)}

∴ C = 1600 + 1600

∴ C = 3200

The cost of the least expensive fence is $3200

Learn more:

You can learn more about the differentiation in brainly.com/question/4279146

#LearnwithBrainly

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