Respuesta :
Given:
The equation of parallel line is
[tex]4x+y-2=0[/tex]
The required line passes through the point (4,-3).
To find:
The equation of required line is standard form.
Solution:
The standard form of a line is
[tex]Ax+By=C[/tex]
Where, A,B,C are constants and the slope of the line is [tex]-\dfrac{A}{B}[/tex].
The given equation is
[tex]4x+y-2=0[/tex]
Here, [tex]A=4,B=1,C=2[/tex]. So, the slope of the line is
[tex]m=-\dfrac{4}{1}[/tex]
[tex]m=-4[/tex]
Slopes of parallel lines are equal. So, the slope of the required line is -4
The required line passes trough the point (4,-3) with slope -4. So, the equation of the required line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-3)=-4(x-4)[/tex]
[tex]y+3=-4x+16[/tex]
Isolate variable terms.
[tex]4x+y=16-3[/tex]
[tex]4x+y=13[/tex]
Therefore, the correct option is A.
