To solve the equation $Y - 2 = \frac{1}{5}(x + 5)$, follow these steps:

Step 1: Isolate $Y$

We want to solve for $Y$. Start by simplifying the right-hand side of the equation.

$Y - 2 = \frac{1}{5}(x + 5)$

Distribute $\frac{1}{5}$ to both terms inside the parentheses:

$Y - 2 = \frac{1}{5}x + 1$

Step 2: Solve for $Y$

Now, add 2 to both sides to isolate $Y$:

$Y = \frac{1}{5}x + 1 + 2$

Simplify the right-hand side:

$Y = \frac{1}{5}x + 3$

So, the final equation is:

$Y = \frac{1}{5}x + 3$

This is the solution in slope-intercept form $Y = mx + b$, where the slope $m = \frac{1}{5}$ and the y-intercept $b = 3$.

Would you like more details or have any questions about the solution? Here are some related questions for further practice:

1. What is the slope of the line in the equation $Y = \frac{1}{5}x + 3$?
2. How do you graph the equation $Y = \frac{1}{5}x + 3$?
3. If $x = 10$, what is the value of $Y$ in the equation?
4. How do you convert the equation to standard form $Ax + By = C$?
5. What is the y-intercept of the line represented by this equation?

Tip: When solving equations involving fractions, distributing first often simplifies the equation.