Answer:
[tex]\[y=-\frac{1}{2}x+\frac{5}{2}\][/tex]
Step-by-step explanation:
Equation of the given line: [tex]\[y=2x-3\][/tex]
Slope of the line = [tex]\[2\][/tex]
Slope of the perpendicular line = [tex]\[-\frac{1}{2}\][/tex]
So the equation of the perpendicular line:
[tex]\[y=-\frac{1}{2}x+c\][/tex]
This passes through the point (-1,2).Substituting in the equation:
[tex]\[2=-\frac{1}{2}*(-1)+c\][/tex]
=> [tex]\[c=2+\frac{1}{2}\][/tex]
=> [tex]\[c=\frac{5}{2}\][/tex]
So the equation of the line :
[tex]\[y=-\frac{1}{2}x+\frac{5}{2}\][/tex]
