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Find the inverse of the function.\newliney=−5x+9y = -5x + 9\newlineWrite your answer in the form ax+bax + b. Simplify any fractions.\newliney=y = ______

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Q. Find the inverse of the function.\newliney=−5x+9y = -5x + 9\newlineWrite your answer in the form ax+bax + b. Simplify any fractions.\newliney=y = ______
  1. Swap xx and yy: To find the inverse of the function, we first swap xx and yy. This gives us the equation x=−5y+9x = -5y + 9.
  2. Solve for y: Next, we need to solve for y. To do this, we add 5y5y to both sides of the equation to get x+5y=9x + 5y = 9.
  3. Isolate yy term: Now, we subtract xx from both sides to isolate the term with yy on one side: 5y=9−x5y = 9 - x.
  4. Divide by 55: To solve for yy, we divide both sides of the equation by 55. This gives us y=9−x5y = \frac{9 - x}{5}.
  5. Simplify further: We can simplify this further by distributing the division across the terms in the numerator: y=95−x5y = \frac{9}{5} - \frac{x}{5}.
  6. Rearrange terms: Finally, we write the inverse function in the form ax+bax + b by rearranging the terms: y=−15x+95y = -\frac{1}{5}x + \frac{9}{5}.

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