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.

Learn how to solve the linear equation Y - 2 = 1/5(x + 5) by using the distributive property and converting it into slope-intercept form. This problem is ideal for students in Grades 6-8 and covers key concepts such as slope and y-intercept.

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