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The given equation is:

\[
12y - 15x = -84
\]

We need to rewrite it in slope-intercept form, which is of the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Isolate \(y\)
First, we solve for \(y\) by moving all terms involving \(x\) to the other side:

\[
12y = 15x - 84
\]

### Step 2: Divide by 12
Next, divide the entire equation by 12 to solve for \(y\):

\[
y = \frac{15x}{12} - \frac{84}{12}
\]

### Step 3: Simplify the fractions
Now simplify each fraction:

\[
y = \frac{5x}{4} - 7
\]

Thus, the equation in slope-intercept form is:

\[
y = \frac{5}{4}x - 7
\]

This is the simplified slope-intercept form of the given equation.

Would you like more details on any part of the process? Here are five related questions to deepen your understanding:

1. How do you find the slope from a linear equation?
2. What is the significance of the y-intercept in a linear equation?
3. How do you convert an equation from standard form to slope-intercept form?
4. Can slope-intercept form be used to easily graph a line? Why?
5. What are the real-life applications of slope-intercept form?

**Tip:** Always simplify fractions when converting to slope-intercept form to ensure your answer is in its simplest form.

Put the following equation of a line into slope-intercept form, simplifying all fractions: 12y - 15x = 84

Learn how to convert the linear equation 12y - 15x = 84 into slope-intercept form y = mx + b, simplifying all fractions. This process covers key algebraic concepts such as isolating variables and simplifying fractions. Suitable for students in Grades 8-10.

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