SOLUTION: Find the equation of the line through the y-intercept of y= x^4-8x^5-9+8x^2 and the x-intercept of y= 11x-4 . Write the coefficients in the form of a simple fraction, if it is nec

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the equation of the line through the y-intercept of y= x^4-8x^5-9+8x^2 and the x-intercept of y= 11x-4 . Write the coefficients in the form of a simple fraction, if it is nec      Log On


   

Question 169661This question is from textbook Wiley: Fuctions Modeling Change
: Find the equation of the line through the y-intercept of y= x^4-8x^5-9+8x^2 and the x-intercept of y= 11x-4 .
Write the coefficients in the form of a simple fraction, if it is necessary. This question is from textbook Wiley: Fuctions Modeling Change

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The y intercept occurs when x=0.
y%280%29=+0%5E4-8%2A0%5E5-9%2B8%280%29%5E2
y%280%29=0-0-9%2B0
y%280%29=-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%2F11
Second point (4/11,0).
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First find the slope,
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%280-%28-9%29%29%2F%284%2F11-0%29
m=%289%29%2F%284%2F11%29
m=99%2F4
Then use the point-slope form of a line,
y-y%5Bp%5D=m%28x-x%5Bp%5D%29
You can use either point.
We'll use (0,-9).
y-%28-9%29=%2899%2F4%29%28x-0%29
y=%2899%2F4%29x-9
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Graph all of the equations to verify the solution.

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.