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For a given input value b, the function f outputs a value a to satisfy the following equation. 4a+7b=-52 Write a formula for f(b) in terms of b. f(b)=◻

For a given input value b b , the function f f outputs a value a a to satisfy the following equation.\newline4a+7b=−52 4a+7b=-52 \newlineWrite a formula for f(b) f(b) in terms of b b .\newlinef(b)=□ f(b)=\square

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Q. For a given input value b b , the function f f outputs a value a a to satisfy the following equation.\newline4a+7b=−52 4a+7b=-52 \newlineWrite a formula for f(b) f(b) in terms of b b .\newlinef(b)=□ f(b)=\square
  1. Given Equation: We are given the equation 4a+7b=−524a + 7b = -52 and need to solve for aa in terms of bb to find the function f(b)f(b).
  2. Isolate 4a4a: First, we isolate the term 4a4a by subtracting 7b7b from both sides of the equation.\newline4a+7b−7b=−52−7b4a + 7b - 7b = -52 - 7b\newlineThis simplifies to:\newline4a=−52−7b4a = -52 - 7b
  3. Divide by 44: Next, we divide both sides of the equation by 44 to solve for aa.a=−52−7b4a = \frac{{-52 - 7b}}{{4}}
  4. Function f(b)f(b): Now we have expressed aa in terms of bb, which gives us the function f(b)f(b).f(b)=−52−7b4f(b) = \frac{{-52 - 7b}}{{4}}

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