Mathematics: Find the equation of the line that is perpendicular to LaTeX: y=-rac{1}{5}x+3y = − 1 5 x + 3 and goes through the point (4, -3). Put your answer in slope intercept form

Find the equation of the line that is perpendicular

alexagyemang440

20.01.2022

y=5x-23

Step-by-step explanation:

step 1

Find the slope of the line that is perpendicular to the given line

we have

$y=-\frac{1}{5}x+3$ -----> given line

The slope of the given line is

$m=-\frac{1}{5}$

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal

therefore

The slope of the line that is perpendicular to the given line is

m=5

step 2

Find the equation of the line in slope intercept form

y=mx+b

we have

$m=5\\point\ (4,-3)$

substitute

-3=5(4)+b

solve for b

b=-23

therefore

y=5x-23

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