# Graph 12xy-28-15y+35 12xy-28-15y+35
Solve for y.
Subtract 7 from both sides of the equation.
12xy-15y=-7
Factor 3y out of 12xy-15y.
Factor 3y out of 12xy.
3y(4x)-15y=-7
Factor 3y out of -15y.
3y(4x)+3y(-5)=-7
Factor 3y out of 3y(4x)+3y(-5).
3y(4x-5)=-7
3y(4x-5)=-7
Divide each term by 3(4x-5) and simplify.
Divide each term in 3y(4x-5)=-7 by 3(4x-5).
3y(4x-5)3(4x-5)=-73(4x-5)
Simplify 3y(4x-5)3(4x-5).
Cancel the common factor of 3.
Cancel the common factor.
3y(4x-5)3(4x-5)=-73(4x-5)
Rewrite the expression.
y(4x-5)4x-5=-73(4x-5)
y(4x-5)4x-5=-73(4x-5)
Cancel the common factor of 4x-5.
Cancel the common factor.
y(4x-5)4x-5=-73(4x-5)
Divide y by 1.
y=-73(4x-5)
y=-73(4x-5)
y=-73(4x-5)
Move the negative in front of the fraction.
y=-73(4x-5)
y=-73(4x-5)
y=-73(4x-5)
Find the asymptotes.
Find where the expression -73(4x-5) is undefined.
x=54
Consider the rational function R(x)=axnbxm where n is the degree of the numerator and m is the degree of the denominator.
1. If n<m, then the x-axis, y=0, is the horizontal asymptote.
2. If n=m, then the horizontal asymptote is the line y=ab.
3. If n>m, then there is no horizontal asymptote (there is an oblique asymptote).
Find n and m.
n=0
m=1
Since n<m, the x-axis, y=0, is the horizontal asymptote.
y=0
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
This is the set of all asymptotes.
Vertical Asymptotes: x=54
Horizontal Asymptotes: y=0
No Oblique Asymptotes
Vertical Asymptotes: x=54
Horizontal Asymptotes: y=0
No Oblique Asymptotes
Graph 12xy-28-15y+35     