Question

What equation is perpendicular to y=2x-3 and
passes through (-1, 2)?

Answer 1

`\[y=-(1)/(2)x+(5)/(2)\]`

Explanation:

Equation of the given line:
`\[y=2x-3\]`

Slope of the line =
`\[2\]`

Slope of the perpendicular line =
`\[-(1)/(2)\]`

So the equation of the perpendicular line:

`\[y=-(1)/(2)x+c\]`

This passes through the point (-1,2).Substituting in the equation:

`\[2=-(1)/(2)*(-1)+c\]`

=>
`\[c=2+(1)/(2)\]`

=>
`\[c=(5)/(2)\]`

So the equation of the line :

`\[y=-(1)/(2)x+(5)/(2)\]`