Write the equation of a line perpendicular to the line x+2y=5 and containing the point (-3, -1). ?

Question

Write the equation of a line perpendicular to the line x+2y=5 and containing the point (-3, -1). ?

Answer 1

x+2y=5

rearranging

2y = -x+5

y = -1/2x +5/2

so  slope here is -1/2 so perpendicular slope is  the negative reciprocal of this - i.e flip over fraction and change sign

m = 2

we also know that x=-3 and y=-1

y=mx+b

-1 = 2*-3+b

-1=-6+b

-1+6=b

5 = b

so

y= 2x+5

Answer 2

find the slope

2y = 5 - x

y = 5/2 - (1/2)x

slope = -1/2

perpendicular slope = 2

y = mx + b

-1 = 2(-3) + b

-1 = -6 + b

5 = b

y = 2x + 5