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

`y=5x-23`

Explanation:

step 1

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

we have

`y=-(1)/(5)x+3` -----> given line

The slope of the given line is

`m=-(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`