Question 169661
The y intercept occurs when x=0.
{{{y(0)= 0^4-8*0^5-9+8(0)^2}}}
{{{y(0)=0-0-9+0}}}
{{{y(0)=-9}}}
First point (0,-9).
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The x intercept occurs when y=0.
{{{y= 11x-4}}} 
{{{0= 11x-4}}} 
{{{11x=4}}}
{{{x=4/11}}}
Second point (4/11,0).
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First find the slope,
{{{m=(y[2]-y[1])/(x[2]-x[1])}}}
{{{m=(0-(-9))/(4/11-0)}}}
{{{m=(9)/(4/11)}}}
{{{m=99/4}}}
Then use the point-slope form of a line,
{{{y-y[p]=m(x-x[p])}}}
You can use either point.
We'll use (0,-9).

{{{y-(-9)=(99/4)(x-0)}}}
{{{y=(99/4)x-9}}}
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Graph all of the equations to verify the solution.
{{{ graph( 300, 300, -2, 2, -10, 10, x^4-8x^5-9+8x^2, 11x-4,(99/4)x-9) }}} 
Red graph is the 4th order polynomial.
Green line is the line.
Blue line is the line from the intercepts of the other two graphs.