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Determine the gradient of a segment in line that connecting points:
X
=
(
4
,
2
)
{\displaystyle \!X=(\!4,\!2)}
and
Y
=
(
−
3
,
−
4
)
{\displaystyle \!Y=(\!-3,\!-4)}
A
=
(
−
5
,
−
2
)
{\displaystyle \!A=(\!-5,\!-2)}
and
B
=
(
3
,
4
)
{\displaystyle \!B=(\!3,\!4)}
α
=
(
5
,
−
3
)
{\displaystyle \alpha =(\!5,\!-3)}
and
β
=
(
−
2
,
8
)
{\displaystyle \beta =(\!-2,\!8)}
λ
=
(
−
6
,
3
)
{\displaystyle \lambda =(\!-6,\!3)}
and
Δ
=
(
4
,
1
)
{\displaystyle \Delta =(\!4,\!1)}
P
=
(
−
4
,
7
)
{\displaystyle \!P=(\!-4,\!7)}
and
Q
=
(
6
,
−
3
)
{\displaystyle \!Q=(\!6,\!-3)}
E
=
(
7
,
5
)
{\displaystyle \!E=(\!7,\!5)}
and
F
=
(
4
,
6
)
{\displaystyle \!F=(\!4,\!6)}
κ
=
(
−
5
,
−
2
)
{\displaystyle \kappa =(\!-5,\!-2)}
and
Ω
=
(
−
4
,
−
9
)
{\displaystyle \Omega =(\!-4,\!-9)}
M
=
(
−
3
,
4
)
{\displaystyle \!M=(\!-3,\!4)}
and
N
=
(
5
,
−
6
)
{\displaystyle \!N=(\!5,\!-6)}
R
=
(
−
5
,
1
)
{\displaystyle \!R=(\!-5,\!1)}
and
S
=
(
−
4
,
−
10
)
{\displaystyle \!S=(\!-4,\!-10)}
C
=
(
3
,
−
5
)
{\displaystyle \!C=(\!3,\!-5)}
and
D
=
(
5
,
−
3
)
{\displaystyle \!D=(\!5,\!-3)}
Find the gradient line from:
x
+
y
=
14
{\displaystyle \!x+\!y=\!14}
3
x
−
5
y
=
11
{\displaystyle \!3x-\!5y=\!11}
5
x
+
4
y
=
41
{\displaystyle \!5x+\!4y=\!41}
x
−
y
=
15
{\displaystyle \!x-\!y=\!15}
3
(
2
x
+
5
y
)
=
3
{\displaystyle \!3(\!2x+\!5y)=\!3}
5
x
−
y
=
18
{\displaystyle \!5x-\!y=\!18}
6
x
+
3
y
=
62
{\displaystyle \!6x+\!3y=\!62}
10
x
−
5
y
=
75
{\displaystyle \!10x-\!5y=\!75}
7
x
+
3
y
=
−
8
{\displaystyle \!7x+\!3y=\!-8}
3
x
−
5
y
=
−
30
{\displaystyle \!3x-\!5y=\!-30}
5
x
+
9
y
=
−
2
{\displaystyle \!5x+\!9y=\!-2}
4
x
+
y
=
0
{\displaystyle \!4x+\!y=\!0}
6
x
−
3
y
=
0
{\displaystyle \!6x-\!3y=\!0}
4
(
3
x
+
y
)
=
8
{\displaystyle \!4(\!3x+\!y)=\!8}
2
x
−
0
,
5
y
=
−
7
{\displaystyle \!2x-\!0,5y=\!-7}
1
,
5
x
+
2
,
5
y
=
21
{\displaystyle \!1,5x+\!2,5y=\!21}
2
,
4
x
+
1
,
5
y
=
14
,
7
{\displaystyle \!2,4x+\!1,5y=\!14,7}
3
,
2
x
−
2
,
3
y
=
5
{\displaystyle \!3,2x-\!2,3y=\!5}
4
,
5
x
+
2
,
7
y
=
18
,
9
{\displaystyle \!4,5x+\!2,7y=\!18,9}
6
,
7
x
−
1
,
9
y
=
19
,
2
{\displaystyle \!6,7x-\!1,9y=\!19,2}
Draw in the Cartesian diagram if known the four points are:
A
=
(
4
,
−
2
)
,
B
=
(
3
,
3
)
,
C
=
(
−
6
,
3
)
,
D
=
(
5
,
4
)
{\displaystyle \!A=\!(\!4,\!-2),\!B=\!(\!3,\!3),\!C=\!(\!-6,\!3),\!D=\!(\!5,\!4)}
A
=
(
−
7
,
−
1
)
,
B
=
(
4
,
−
2
)
,
C
=
(
−
1
,
−
9
)
,
D
=
(
−
4
,
3
)
{\displaystyle \!A=\!(\!-7,\!-1),\!B=\!(\!4,\!-2),\!C=\!(\!-1,\!-9),\!D=\!(\!-4,\!3)}
A
=
(
−
5
,
5
)
,
B
=
(
6
,
−
6
)
,
C
=
(
−
3
,
3
)
,
D
=
(
2
,
−
2
)
{\displaystyle \!A=\!(\!-5,\!5),\!B=\!(\!6,\!-6),\!C=\!(\!-3,\!3),\!D=\!(\!2,\!-2)}
A
=
(
1
,
−
10
)
,
B
=
(
−
3
,
−
6
)
,
C
=
(
4
,
7
)
,
D
=
(
−
6
,
1
)
{\displaystyle \!A=\!(\!1,\!-10),\!B=\!(\!-3,\!-6),\!C=\!(\!4,\!7),\!D=\!(\!-6,\!1)}
A
=
(
−
2
,
−
2
)
,
B
=
(
−
5
,
7
)
,
C
=
(
1
,
3
)
,
D
=
(
−
9
,
5
)
{\displaystyle \!A=\!(\!-2,\!-2),\!B=\!(\!-5,\!7),\!C=\!(\!1,\!3),\!D=\!(\!-9,\!5)}
From the questions number 3, calculate the gradient of line AB and line CD.
From the questions number 3, are the both lines parallel? If not, give the reason.