Respuesta :
The equation of a line perpendicular to the line [tex]m[/tex] is [tex]y=-\frac{3}{2}x+5[/tex]
Slope of two perpendicular lines
Two perpendicular lines' slopes are negative reciprocals of each other.
For example, if a line is perpendicular to a line that has a slope [tex]m[/tex], then the slope of the line is [tex]-\frac{1}{m}[/tex].
How to find the equation of a line perpendicular to the given line?
The equation for the line [tex]m[/tex] is [tex]y=-\frac{2}{3}x+5[/tex]
The slope of a line [tex]m[/tex] is [tex]-\frac{2}{3}[/tex]
The slope of a line that is perpendicular to the line m is [tex]-\frac{1}{\frac{2}{3} }[/tex]
That is [tex]-\frac{3}{2}[/tex]
Thus, the equation of a line perpendicular to the given line is [tex]y=-\frac{3}{2}x+5[/tex]
Hence, option (C) is correct.
Learn more about the slope of perpendicular lines here-
https://brainly.com/question/10431875
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