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Lubov Fominskaja [6]
3 years ago
5

Complete the equation of the line through (-6, -5) and (-4, -4). Use exact numbers

Mathematics
1 answer:
77julia77 [94]3 years ago
3 0


In general the equation through (a,b) and (c,d) is


(y-b)(c-a)=(x-a)(d-b)


Can you see that this is a line and that both (a,b) and (c,d) are on it?


Here we're given (a,b)=(-6,-5) and (c,d)=(-4,-4)


(y- -5)(-4 - -6) = (x - -6)(-4 - 5)


2(y+5)=x+6


2y + 10 = x + 6


x - 2y  = 4


y = \frac 1 2 x - 2


Either of the last two are fine answers.





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Answer:

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Step-by-step explanation:

Solve the following system:

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Express the system in matrix form:

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3 | -4)(x

y) = (-6

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Solve the system with Cramer's rule:

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-18 | -4/6 | 2

3 | -4 and y = 6 | -6

3 | -18/6 | 2

3 | -4

Evaluate the determinant 6 | 2

3 | -4 = -30:

x = -6 | 2

-18 | -4/(-30) and y = 6 | -6

3 | -18/(-30)

Simplify -6 | 2

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x = -1/30 -6 | 2

-18 | -4 and y = 6 | -6

3 | -18/(-30)

Simplify 6 | -6

3 | -18/(-30):

x = -(-6 | 2

-18 | -4)/30 and y = -1/30 6 | -6

3 | -18

Evaluate the determinant -6 | 2

-18 | -4 = 60:

x = (-1)/30×60 and y = -(6 | -6

3 | -18)/30

(-1)/30×60 = -2:

x = -2 and y = -(6 | -6

3 | -18)/30

Evaluate the determinant 6 | -6

3 | -18 = -90:

x = -2 and y = (-1)/30×-90

(-1)/30 (-90) = 3:

Answer: x = -2 and y = 3

___________________________________________

Solve the following system:

{y = -3 x - 3

y = (3 x)/4 + 9/2

Express the system in standard form:

{3 x + y = -3

-(3 x)/4 + y = 9/2

Express the system in matrix form:

(3 | 1

-3/4 | 1)(x

y) = (-3

9/2)

Write the system in augmented matrix form and use Gaussian elimination:

(3 | 1 | -3

-3/4 | 1 | 9/2)

Add 1/4 × (row 1) to row 2:

(3 | 1 | -3

0 | 5/4 | 15/4)

Multiply row 2 by 4/5:

(3 | 1 | -3

0 | 1 | 3)

Subtract row 2 from row 1:

(3 | 0 | -6

0 | 1 | 3)

Divide row 1 by 3:

(1 | 0 | -2

0 | 1 | 3)

Collect results:

Answer:  {x = -2 , y = 3

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