Respuesta :
Answer: The equation of a line parallel to the line x=3 that passes through the point (-4,-3) is x = -4.
Solution
The given line x=3 (x=constant) is a vertical line. A line parallel to this line must be a vertical line with equation x=constant, that means the value of x is always the same. Like this line passes through the point (-4,-3) with abscissa x=-4, this abscissa must be constant, then the equation of this line must be x = -4
we are given
a line parallel to the line x=3
It means that line will be vertical line
and we know that slope of vertical line is always infinity
so,
[tex]m=\infty[/tex]
[tex]m=\frac{1}{0}[/tex]
now, it passes through the point (-4,-3)
so, we can use point slope form of line
[tex]y-y_1=m(x-x_1)[/tex]
we can plug values
[tex]y+3=\frac{1}{0}(x+4)[/tex]
we can cross multiply
and we get
[tex]0\times (y+3)=1\times (x+4)[/tex]
[tex]0=(x+4)[/tex]
Subtract both sides by 4
[tex]0-4=(x+4)-4[/tex]
[tex]x=-4[/tex]
So, the equation of line is x=-4..........Answer
