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Find the inverse of the function.\newliney=−5x−7y = -5x - 7\newlineWrite your answer in the form ax+bax + b. Simplify any fractions.\newliney=y = ______

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Full solution

Q. Find the inverse of the function.\newliney=−5x−7y = -5x - 7\newlineWrite your answer in the form ax+bax + b. Simplify any fractions.\newliney=y = ______
  1. Swap x and y: Swap xx and yy in the equation y=−5x−7y = -5x - 7 to begin finding the inverse function.\newlineNew function: x=−5y−7x = -5y - 7
  2. Add 77 to isolate y: Add 77 to both sides of the equation x=−5y−7x = -5y - 7 to isolate the term with yy.\newlinex+7=−5y−7+7x + 7 = -5y - 7 + 7\newlineSimplify the equation to get x+7=−5yx + 7 = -5y.
  3. Divide by −5 -5 for y y : Divide both sides of the equation x+7=−5y x + 7 = -5y by −5 -5 to solve for y \.\newlinex+7−5=y\frac{x + 7}{ -5} = y\newlineSimplify the equation to get y=−x+75 y = -\frac{x + 7}{ 5}.
  4. Rewrite in ax+bax + b form: Rewrite the equation y=−x+75y = -\frac{x + 7}{5} in the form ax+bax + b. Distribute the negative sign to get y=−x5−75y = -\frac{x}{5} - \frac{7}{5}.

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