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patriot [66]
3 years ago
12

Find the equation of the line that passes through the points (6,1) and (3,4)

Mathematics
1 answer:
IrinaK [193]3 years ago
8 0
(6,1) , (3,4)
slope = (4 - 1) / (3 - 6) = -3/3 = -1

y = mx + b
slope(m) = -1
use either of ur points....(6,1)...x = 6 and y = 1
now sub and find b, the y int
1 = -1(6) + b
1 = -6 + b
1 + 6 = b
7 = b

so ur equation is : y = -x + 7

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The answer: m∡BCD = 130° .
_____________________________________
Explanation:
______________________________
m∡BCD = 9x - 5 = our answer.
_____________________________
Note: (9x - 5) + (m∡C IN Δ  ACB)= 180 ;
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Reason: all angles on straight line add up to 180.
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Note: In Δ ACB; m∡A + m∡B + m∡c = 180.
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Reason: All three angles in any triangle add up to 180.
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Given  Δ ACB, we are given:
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m∡C= ?
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m∡A = 65
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So, given  Δ ACB; m∡A + m∡B + m∡c = 180;
 →Plug in our known values and rewrite:
___________________________________
Given  Δ ACB; 65 + 4x + 5 + (m∡c) = 180;
  →Simplify, and rewrite:
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Given  Δ ACB; 4x + 70 + (m∡c) = 180;
  →Subtract "70" from each side of the equation; and rewrite:
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Given  Δ ACB; 4x + (m∡C) = 110;
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______________________________________________
Given Δ ACB' m∡C = 110 - 4x ;
__________________________________________
So, we know that: (110 - 4x) + (9x - 5) = 180; (since all angles on a straight line add up to 180.
____________________
We can solve for "x".
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(110 - 4x) + (9x - 5) = 180;
________________________
Rewrite as: 
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(110 - 4x) + 1(9x - 5) = 180 ;  (Note: there is an implied coefficient of "1"; since anything multiplied by "1" equals that same value).
_______________________
Note the "distributive property of multiplication": 
_________________
 a*(b+c) = ab + ac ; AND:
 a*(b - c) = ab - ac .
_______________________
So, +1(9x - 5) = (+1*9x) - (+1*5) = 9x - 5 ;
__________________________
So we can rewrite:
___________________
(110 - 4x) + (9x - 5) = 180 ; as:
________________________
110 - 4x + 9x - 5 = 180 ;  We can simplify this by combining "like terms" on                                         the "left-hand side" of the equation:
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110 - 5 = 105 ;
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So, rewrite as: 5x + 105 = 180;  Subtract "105" from EACH side; to get:
_____________________________________
 5x  = 75 ; Now, divide each side of the equation by "5"; 
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_____________________________________________
Now, we want to know: m∡BCD; which equals:
_____________________________________________
 9x - 5 ;  let us substitute "15" for "x"; and solve:
______________________
9x - 5 = 9*(15) - 5 = 135 - 5 = 130.
_____________________________
The answer: m∡BCD = 130°
________________________
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