Answer :
We know that two lines are perpendicular if and only if their slopes fullfil:
[tex]m_1m_2=-1[/tex]Then we need to find the slope of the equation given:
[tex]y=x+4[/tex]we notice that this equation is written in the slope intercept form:
[tex]y=mx+b[/tex]comparing this equations we notice that:
[tex]m_1=1[/tex]Now, plugging this value in the condition and solving for the second slope we have:
[tex]\begin{gathered} 1m_2=-1 \\ m_2=-\frac{1}{1} \\ m_2=-1 \end{gathered}[/tex]Now that we have the slope of the line we are looking form we plug its value, and the point in the equation:
[tex]y-y_1=m(x-x_1)[/tex]then:
[tex]\begin{gathered} y-(-2)=-1(x-3) \\ y+2=-x+3 \end{gathered}[/tex]finally we write the equation in the slope intercept form given above:
[tex]\begin{gathered} y+2=-x+3 \\ y=-x+3-2 \\ y=-x+1 \end{gathered}[/tex]Therefore the equation we are looking for is:
[tex]y=-x+1[/tex]