Explanation
The slope-intercept equation of a line has the form
[tex]y=m\cdot x+b,[/tex]
where m is the slope of the line and b is its y-intercept.
Now, there is a very interesting relationship between the slopes (m_1 and m_2) of perpendicular lines:
[tex]m_1=-\frac{1}{m_2}\text{.}[/tex]
Looking at the given equation, we can say that its slope is 1/2. Then,
[tex]m=-\frac{1}{\frac{1}{2}}=-2.[/tex]
Then, our desired equation becomes
[tex]y=-2x+b\text{.}[/tex]
Now, we know that our line passes through (-2,5). This means that
[tex]5=-2\cdot(-2)+b\text{.}[/tex]
Solving this equation for b, we get
[tex]\begin{gathered} 5=4+b, \\ 4+b=5, \\ b=5-4, \\ b=1. \end{gathered}[/tex]
AnswerThe desired line has equation
[tex]y=-2x+1.[/tex]
