Find the equation of the line in general form perpendicular to 4x + 37 + 8 = 0 and its distance to a point (6,2) is 3 units with solution.

Answer 1

Odds are you hit 7 mistakenly when you typed "y"

4x + 3y + 8 = 0

3y = -4x -8

y = -4x/3 -8/3 has a perpendicular liine with negative inverse slope

y = 3x/4 + b which is 3 units from (6,2)

two perpendicular lines are within 3 units of (6,2)

15x-20y -19 =0

and

15x-20y +17 =0

plot the point and lines

construct some right triangles

and use the distance formula (version of the pythagorean formula) to calculate 3 units

the perpendicular lines intersect at (9/5,-2/5) and (21/5,22/5) or (1.8,-0.4) and (4.2,4.4)

3^2 = 1.8^2 +2.4^2 = 3.24+5.76 = 9

sqr9 = 3 units from both points of intersection