Answer:
[tex]y=-2x-3[/tex]
Step-by-step explanation:
we know that
If two lines are perpendicular
then
the product of their slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
Step 1
Find the slope of the given line
we have
[tex]y=\frac{1}{2}x-5[/tex]
the slope of the given line is equal to
[tex]m1=\frac{1}{2}[/tex]
Step 2
Find the slope of the line perpendicular to the given line
[tex]\frac{1}{2}*m2=-1[/tex]
[tex]m2=-2[/tex]
Step 3
Find the equation of the line into slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-2[/tex]
[tex]point(2,-7)[/tex]
substitute and solve for b
[tex]-7=-2*(2)+b[/tex]
[tex]-7=-4+b[/tex]
[tex]b=-7+4=-3[/tex]
The equation of the line is equal to
[tex]y=-2x-3[/tex]
