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For a given input value x, the function g outputs a value y to satisfy the following equation. -4x-6=-5y+2 Write a formula for g(x) in terms of x. g(x)=◻

For a given input value xx, the function gg outputs a value yy to satisfy the following equation.\newline−4x−6=−5y+2-4x-6=-5y+2\newlineWrite a formula for g(x)g(x) in terms of xx.\newlineg(x)=□g(x)=\square

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Q. For a given input value xx, the function gg outputs a value yy to satisfy the following equation.\newline−4x−6=−5y+2-4x-6=-5y+2\newlineWrite a formula for g(x)g(x) in terms of xx.\newlineg(x)=□g(x)=\square
  1. Isolate y in the equation: First, we need to isolate y on one side of the equation to solve for g(x) in terms of x. The given equation is −4x−6=−5y+2-4x - 6 = -5y + 2.
  2. Move terms involving y to one side: Add 55y to both sides of the equation to move the terms involving y to one side: −4-4x - 66 + 55y = 22.
  3. Move constant term to the other side: Now, subtract 22 from both sides to move the constant term to the other side: −4x−6+5y−2=0-4x - 6 + 5y - 2 = 0.
  4. Combine like terms: Combine like terms on the left side of the equation: −4x−8+5y=0-4x - 8 + 5y = 0.
  5. Isolate the term with yy: Add 4x+84x + 8 to both sides to isolate the term with yy: 5y=4x+85y = 4x + 8.
  6. Solve for y: Finally, divide both sides by 55 to solve for yy: y=4x+85y = \frac{4x + 8}{5}.
  7. Write the function g(x) g(x) : Since g(x) g(x) outputs y y , we can write the function as g(x)=4x+85 g(x) = \frac{4x + 8}{5} .

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