Question

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

Answer 1

Answer:

$y=5x-23$

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

$y=5x-23$