Answer:
[tex]y=-\frac{1}{2}x+\frac{13}{2}[/tex]
Step-by-step explanation:
step 1
Find the slope of the given line
we have
[tex]y=2x+4[/tex]
the slope m is equal to
[tex]m=2[/tex]
step 2
Find the slope of the perpendicular line to the given line
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
so
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=2[/tex]
[tex](2)*m_2=-1[/tex]
[tex]m_2=-\frac{1}{2}[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{2}[/tex]
[tex]point\ (3,5)[/tex]
substitute
[tex]y-5=-\frac{1}{2}(x-3)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
[tex]y-5=-\frac{1}{2}x+\frac{3}{2}[/tex]
[tex]y=-\frac{1}{2}x+\frac{3}{2}+5[/tex]
[tex]y=-\frac{1}{2}x+\frac{13}{2}[/tex]
