Find the equation of the line perpendicular to the line 3x + y−4=0 and containing point (1, −5).

Step-by-step explanation:

Write 3x + y - 4 = 0 in the form of y = mx + c ,

where m is is the gradient .

Thus, y = -3x + 4

Next use the formula,

m1 × m2 = -1

to find the gradient for the new equation.

-3 × m2 = -1

m2 = 1/3

Given the contacting point (1, -5), therefore

y-(-5) =1/3(x-1)

y+5=1/3(x) - 1/3

y = 1/3(x) -1/3 -5

y = 1/3 (x) -16/3

vertical asymptote .

horizontal asymptote .

step-by-step explanation:

given function is .

vertical asymptote is given by setting

denominator =0

when degree of numerator and denominator are same then divide first term of numerator by first term of denominator to get horizontal asymptote.