Find the inverse of the function. y = 5x + 6 Write your answer in the form ax + b. Simplify any fractions. y = ______

Swap x and y: To find the inverse of the function, we first swap x and y. This gives us the equation x = 5y + 6.Solve for y: Next, we need to solve for y. To do this, we subtract 6 from both sides of the equation to isolate the term with y. This gives us x - 6 = 5y + 6 - 6.Isolate y: Simplifying the equation, we get x - 6 = 5y. Now we need to isolate y by dividing both sides of the equation by 5.Divide by 5: Dividing both sides by 5 gives us (x - 6) / 5 = y. This is the inverse function in the form y = ax + b.Write in ax + b form: To write it in the form ax + b, we can express it as y = (1/5)x - 6/5. This is the simplified form of the inverse function.

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Find the inverse of the function. $\newline$ $y = 5x + 6$ $\newline$ Write your answer in the form $ax + b$ . Simplify any fractions. $\newline$ $y =$ ______

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Algebra 1

Find the inverse of a linear function

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Q. Find the inverse of the function.

\newline

y = 5x + 6

\newline

Write your answer in the form

ax + b

. Simplify any fractions.

\newline

y =

______

Swap $x$ and $y$ : To find the inverse of the function, we first swap $x$ and $y$ . This gives us the equation $x = 5y + 6$ .
Solve for y: Next, we need to solve for $y$ . To do this, we subtract $6$ from both sides of the equation to isolate the term with $y$ . This gives us $x - 6 = 5y + 6 - 6$ .
Isolate y: Simplifying the equation, we get $x - 6 = 5y$ . Now we need to isolate $y$ by dividing both sides of the equation by $5$ .
Divide by $5$ : Dividing both sides by $5$ gives us $(x - 6) / 5 = y$ . This is the inverse function in the form $y = ax + b$ .
Write in $ax + b$ form: To write it in the form $ax + b$ , we can express it as $y = \frac{1}{5}x - \frac{6}{5}$ . This is the simplified form of the inverse function.