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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 $x$ , the function $g$ outputs a value $y$ to satisfy the following equation. $\newline$ $-4x-6=-5y+2$ $\newline$ Write a formula for $g(x)$ in terms of $x$ . $\newline$ $g(x)=\square$

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Write equations of cosine functions using properties

Full solution

Q. For a given input value

x

, the function

g

outputs a value

y

to satisfy the following equation.

\newline

-4x-6=-5y+2

\newline

Write a formula for

g(x)

in terms of

x

.

\newline

g(x)=\square

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 $-4x - 6 = -5y + 2$ .
Move terms involving $y$ to one side: Add $5$ y to both sides of the equation to move the terms involving $y$ to one side: $-4$ x - $6$ + $5$ y = $2$ .
Move constant term to the other side: Now, subtract $2$ from both sides to move the constant term to the other side: $-4x - 6 + 5y - 2 = 0$ .
Combine like terms: Combine like terms on the left side of the equation: $-4x - 8 + 5y = 0$ .
Isolate the term with $y$ : Add $4x + 8$ to both sides to isolate the term with $y$ : $5y = 4x + 8$ .
Solve for y: Finally, divide both sides by $5$ to solve for $y$ : $y = \frac{4x + 8}{5}$ .
Write the function $g(x)$ : Since $g(x)$ outputs $y$ , we can write the function as $g(x) = \frac{4x + 8}{5}$ .

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