Mathematics: Through: (-5, 5), perp. to y = 5/9x - 4

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Through: (-5, 5), perp. to y = 5/9x - 4

dude3328

15.01.2022

$y=-\frac{9}{5}x-4$

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

$y=\frac{5}{9}x-4$

The slope of the given line is

$m_1=\frac{5}{9}$

The opposite reciprocal is equal to

$m_2=-\frac{9}{5}$ ----> slope of the perpendicular line

step 2

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

$m=-\frac{9}{5}$

$point\ (-5,5)$

substitute

$y-5=-\frac{9}{5}(x+5)$

step 3

Convert to slope intercept form

Isolate the variable y

$y-5=-\frac{9}{5}(x+5)\\\\y-5=-\frac{9}{5}x-9\\\\y=-\frac{9}{5}x-9+5\\\\y=-\frac{9}{5}x-4$

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