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
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
Slope of the line
[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Given points are (1,3) , ( -3,-5)
[tex]m = \frac{-5-3 }{-3-1 } = \frac{-8}{-4} = 2[/tex]
The equation of the straight line is
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
[tex]y - 3 = 2 ( x - 1 )[/tex]
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
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
Slope of the line
[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Given points are (1,4) , ( 6,-1)
[tex]m = \frac{-1-(4) }{6-1 } = \frac{-5}{5} = -1[/tex]
The equation of the straight line is
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
[tex]y - 1 = -1 ( x - 4 )[/tex]
y - 1 = - x +4
The equation of the straight line is x + y -5 =0
7)
The equation of the straight line is
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
Slope of the line
[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Given points are (-12 , 14) , ( 6,-1)
[tex]m = \frac{-1-(14) }{6+12 } = \frac{-15}{18} = \frac{-5}{6}[/tex]
[tex]y - 14 = \frac{-5}{6} ( x - (-12) )[/tex]
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
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
Slope of the line
[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Given points are (-4 , -2) , ( 4 , 0)
[tex]m = \frac{0+2}{4 +4} = \frac{2}{8} = \frac{1}{4}[/tex]
[tex]y - (-2) =\frac{1}{4} ( x - (-4) )[/tex]
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
