Answer:
[tex]y=-\frac{9}{5}x-4[/tex]
Step-by-step explanation:
The complete question is:
Find the equation of the line that passes through: (-5, 5), and is perpendicular to the line y = 5/9x - 4
step 1
Find the slope of the line
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
The equation of the given line is
[tex]y=\frac{5}{9}x-4[/tex]
The slope of the given line is
[tex]m_1=\frac{5}{9}[/tex]
The opposite reciprocal is equal to
[tex]m_2=-\frac{9}{5}[/tex] ----> slope of the perpendicular line
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{9}{5}[/tex]
[tex]point\ (-5,5)[/tex]
substitute
[tex]y-5=-\frac{9}{5}(x+5)[/tex]
step 3
Convert to slope intercept form
Isolate the variable y
[tex]y-5=-\frac{9}{5}(x+5)\\\\y-5=-\frac{9}{5}x-9\\\\y=-\frac{9}{5}x-9+5\\\\y=-\frac{9}{5}x-4[/tex]
