Respuesta :
Answer:
y = -1/2c - 8
Step-by-step explanation:
2c - y = 6
2c -6 = y
Slope: 2. Slope of the perpendicular line: -1/2
Point (-4,-6)
y-intercept = -6 - (-1/2)(-4)
b = -6 -2 = -8
The equation of the line that passes through the point [tex](-4,-6)[/tex] and is
perpendicular to the line [tex]2c - y = 6[/tex] is [tex]2x_{2} -y_{2} +2=0[/tex].
What is equation of the line ?
Equation of the line: The general equation of a straight line is [tex]y = mx + c[/tex]. This variable [tex]'c'[/tex] is called the intercept on the [tex]y-axis[/tex]. And [tex]y = c[/tex] is the value where the line cuts the [tex]y-axis[/tex].
Here,
[tex]m=[/tex] the gradient,
[tex]c=[/tex] the intercept on the y-axis
We have,
An equation of the line that passes through the point [tex](-4,-6)[/tex] and is
perpendicular to the line [tex]2c - y = 6[/tex] .
So,
Line [tex]2c - y = 6[/tex]
[tex]2c - y = 6[/tex]
⇒ [tex]y=2c-6[/tex]
and [tex]y = mx + c[/tex]
On comparing above two equations
[tex]m=2[/tex]
and Slope [tex]=-\frac{1}{m}[/tex]
So, Slope [tex]=-\frac{1}{2}[/tex]
Now,
Slope of the equation [tex](m)=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Slope of required equation [tex]=\frac{-1}{Slope \ of \ 2c-y=6}[/tex]
[tex]=\frac{-1}{\frac{(-1)}{2} }=2[/tex]
Now,
Equation of line with slope [tex]2[/tex] and passing through point [tex](-4,-6)[/tex] ,
Slope of the equation [tex](m)=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]2=\frac{y_{2} -(-6) }{x_{2} -(-4) }[/tex]
[tex]2x_{2} +8=y_{2} +6[/tex]
[tex]2x_{2} -y_{2} +2=0[/tex]
So, the equation of the line is [tex]2x_{2} -y_{2} +2=0[/tex] .
Hence, we can say that the equation of the line that passes through the point [tex](-4,-6)[/tex] and is perpendicular to the line [tex]2c - y = 6[/tex] is [tex]2x_{2} -y_{2} +2=0[/tex].
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