Answer:
5) The equation of the straight line is 2 x - y + 1 =0
6) The equation of the straight line is x + y -5 =0
7) The equation of the straight line is 5 x + 6 y - 24 =0
8) The equation of the straight line is x - 4 y -4 =0
9) The equation of the parallel line is 3x + y -19 =0
Step-by-step explanation:
5)
The equation of the straight line is

Slope of the line
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Given points are (1,3) , ( -3,-5)

The equation of the straight line is
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
y = 2x - 2 +3
2 x - y + 1 =0
The equation of the straight line is 2 x - y + 1 =0
6)
The equation of the straight line is

Slope of the line

Given points are (1,4) , ( 6,-1)

The equation of the straight line is


y - 1 = - x +4
The equation of the straight line is x + y -5 =0
7)
The equation of the straight line is

Slope of the line

Given points are (-12 , 14) , ( 6,-1)


6( y - 14 ) = - 5 ( x +12 )
6 y - 84 = - 5x -60
5 x + 6 y -84 + 60 =0
5 x + 6 y - 24 =0
8)
The equation of the straight line is

Slope of the line

Given points are (-4 , -2) , ( 4 , 0)


4 ( y + 2) = x + 4
x - 4 y -4 =0
9)
The equation of the line y = 3x + 6 is parallel to the line
3x + y + k =0 is passes through the point ( 4,7 )
⇒ 3x + y + k =0
⇒ 12 + 7 + k =0
⇒ k = -19
The equation of the parallel line is 3x + y -19 =0