Let's solve the equation \( 12y - 15x = 84 \) for \( y \).

### Step 1: Isolate the term with \( y \)
To isolate the \( y \)-term, add \( 15x \) to both sides of the equation:
\[
12y = 15x + 84
\]

### Step 2: Solve for \( y \)
Now, divide the entire equation by 12 to solve for \( y \):
\[
y = \frac{15x + 84}{12}
\]

### Step 3: Simplify the expression
Simplify the terms inside the fraction:
\[
y = \frac{15x}{12} + \frac{84}{12} = \frac{5x}{4} + 7
\]

So the solution for \( y \) is:
\[
y = \frac{5x}{4} + 7
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the slope of a linear equation?
2. Can you rewrite the equation in standard form?
3. How do you graph the equation \( y = \frac{5x}{4} + 7 \)?
4. What is the y-intercept of the equation?
5. How do you find the x-intercept of this equation?

**Tip:** Always simplify expressions as much as possible to make further calculations easier.

Learn how to solve the linear equation 12y - 15x = 84 step-by-step, isolating y in terms of x. This problem covers algebraic manipulation, linear equations, and simplifying expressions. Suitable for students in Grades 8-10.

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