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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)=

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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)=
  1. Isolate y in the equation: First, we need to isolate y on one side of the equation to find the function g(x) in terms of x. We start with the given equation:\newline−4x−6=−5y+2-4x - 6 = -5y + 2
  2. Move the term involving y to the left side: Next, we add 5y5y to both sides of the equation to move the term involving y to the left side:\newline−4x−6+5y=−5y+2+5y-4x - 6 + 5y = -5y + 2 + 5y\newlineThis simplifies to:\newline−4x−6+5y=2-4x - 6 + 5y = 2
  3. Isolate the terms with y on the left side: Now, we subtract 22 from both sides to isolate the terms with yy on the left side:\newline−4x−6+5y−2=2−2-4x - 6 + 5y - 2 = 2 - 2\newlineThis simplifies to:\newline−4x−8+5y=0-4x - 8 + 5y = 0
  4. Get y by itself: We then add 4x+84x + 8 to both sides to get y by itself:\newline5y=4x+85y = 4x + 8
  5. Solve for y: Finally, we divide both sides by 55 to solve for yy:\newliney=4x+85y = \frac{4x + 8}{5}\newlineThis gives us the function g(x)g(x) in terms of xx:\newlineg(x)=4x+85g(x) = \frac{4x + 8}{5}

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