Final answer:
The equation of such a line for the graph of y= x-10/3x^2+x+1 is 3x^2y + xy + y - x + 10 = 0.
Step-by-step explanation:
The equation of the line for the graph of y = (x - 10)/(3x^2 + x + 1) can be found by rearranging the given equation.
First, simplify the expression by combining like terms:
y = (x - 10)/(3x^2 + x + 1)
y = x-10/3x^2+x+1
Next, multiply both sides of the equation by the denominator to eliminate the fraction:
(3x^2 + x + 1)y = (x - 10)
Finally, distribute and rearrange the equation:
3x^2y + xy + y = x - 10
So, the equation of the line is 3x^2y + xy + y - x + 10 = 0.