Graph -x(-3y+13)+5y=11

Math
-x(-3y+13)+5y=11
Solve for y.
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Add 13x to both sides of the equation.
3xy+5y=11+13x
Factor y out of 3xy+5y.
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Factor y out of 3xy.
y(3x)+5y=11+13x
Factor y out of 5y.
y(3x)+y⋅5=11+13x
Factor y out of y(3x)+y⋅5.
y(3x+5)=11+13x
y(3x+5)=11+13x
Divide each term by 3x+5 and simplify.
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Divide each term in y(3x+5)=11+13x by 3x+5.
y(3x+5)3x+5=113x+5+13x3x+5
Cancel the common factor of 3x+5.
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Cancel the common factor.
y(3x+5)3x+5=113x+5+13x3x+5
Divide y by 1.
y=113x+5+13x3x+5
y=113x+5+13x3x+5
Combine the numerators over the common denominator.
y=11+13x3x+5
y=11+13x3x+5
y=11+13x3x+5
Find the asymptotes.
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Find where the expression 11+13x3x+5 is undefined.
x=-53
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=1
m=1
Since n=m, the horizontal asymptote is the line y=ab where a=13 and b=3.
y=133
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=-53
Horizontal Asymptotes: y=133
No Oblique Asymptotes
Vertical Asymptotes: x=-53
Horizontal Asymptotes: y=133
No Oblique Asymptotes
Graph -x(-3y+13)+5y=11

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