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lianna [129]
3 years ago
5

Given a line with a slope of1/2 and a point(6,5) which lies on that find an equation to represent that line

Mathematics
1 answer:
kondor19780726 [428]3 years ago
8 0

Answer:

The equation of the line is given as  2 y - x = 4.

Step-by-step explanation:

Here, the slope of the given line = 1/2

The point  on the line is (x0,y0) = (6,5)

Now, by POINT SLOPE FORMULA:

The equation of line with (x0,y0) and slope m is written as:

(y - y0) = m (x-x0)

So, here the equation of line is given as

( y- 5) = \frac{1}{2} (x-6)\\\implies 2( y-5) = ( x-6)\\or, 2y - 10 = x - 6\\\implies  2y - x = 4

Hence the equation of the line is 2 y - x = 4.

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Adam is building a computer desk with a separate compartment for the computer. The compartment for the computer is a rectangular
Alik [6]

Answer:

The width of the computer compartment is 9 inches

The length of the computer compartment is 33 inches

The height of the computer compartment is 27 inches

Step-by-step explanation:

The given data on the rectangular prism compartment are;

The volume of the rectangular prism, V = 8019 cubic inches

The length of the compartment, l = 24 inches + The width, w

The height of the compartment, h = 18 inches + The width, w

Therefore, we have;

l = 24 + w

h = 18 + w

V = l × h × w

∴ V = (24 + w) × (18 + w) × w = w³ + 42·w² + 432·w = 8019

w³ + 42·w² + 432·w - 8019 = 0

By graphing the above function with MS Excel, we have one of the solution is w = 9

∴ (w - 9) is a factor of w³ + 42·w² + 432·w - 8019 = 0

Dividing, we get;

w² + 51·w + 891

w³ + 42·w² + 432·w - 8019 = 0

w³ - 9·w²

     51·w² - 459·w

                 891·w

                 891·w + 8019

                             0

Therefore,

w³ + 42·w² + 432·w - 8019 = 0

w³ + 42·w² + 432·w - 8019  = (x - 9)·(w² + 51·w + 891) = 0

The determinant of the factor, w² + 51·w + 891 = 51² - 4×1×891 = -963, therefore, the it has complex roots

Therefore, the real solution of (x - 9)·(w² + 51·w + 891) = 0 is w = 9

The width of the computer compartment, w = 9 inches

The length of the computer compartment, l = 24 inches + 9 inches = 33 inches

The height of the computer compartment, h = 18 inches + 9 inches = 27 inches.

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If two variables have a positive linear correlation is the slope of the regression line for the variables positive or​ negative?
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