The equation of a line that is perpendicular to the line [tex]x-2y = 8[/tex] is [tex]y = -2x-4[/tex].
Given that,
Equation of line; x - 2y = 8,
We have to determine,
An equation that is perpendicular to the given equation.
According to the question,
Equation of line;[tex]x - 2y = 8,[/tex]
Convert the given equation in the standard form of [tex]y = mx+c.[/tex]
Then,
[tex]x - 2y = 8 \\\\2y = 8+x\\\\y = \dfrac{x}{2}-4[/tex]
The slope of the line is m = 1/2.
Therefore,
The slope of the required line is perpendicular to another line by finding the opposite reciprocal of the slope.
[tex]m = -2[/tex]
The required equation of a line is, [tex]y = -2x-4[/tex].
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