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Find the inverse of the function.\newliney=−5x−3y = -5x - 3\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−3y = -5x - 3\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−3x = -5y - 3.
  2. Solve for y: Next, we need to solve for y. To do this, we add 33 to both sides of the equation to isolate the term with yy. This gives us x+3=−5y−3+3x + 3 = -5y - 3 + 3.
  3. Isolate yy: Simplifying the equation, we get x+3=−5yx + 3 = -5y. Now, we need to get yy by itself on one side of the equation.
  4. Divide by −5-5: To isolate yy, we divide both sides of the equation by −5-5. This gives us x+3−5=y\frac{x + 3}{-5} = y.
  5. Simplify the fraction: Simplifying the fraction, we get y=−15x−35y = -\frac{1}{5}x - \frac{3}{5}. This is the inverse function in the form ax+bax + b.

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