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To write the equation \( 9x + 5y = 15 \) in slope-intercept form, we need to solve for \( y \) and express it in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Let's go step by step:

### Step 1: Start with the given equation
\[
9x + 5y = 15
\]

### Step 2: Isolate the \( y \)-term by subtracting \( 9x \) from both sides
\[
5y = -9x + 15
\]

### Step 3: Solve for \( y \) by dividing the entire equation by 5
\[
y = \frac{-9}{5}x + \frac{15}{5}
\]

### Step 4: Simplify the constant term
\[
y = \frac{-9}{5}x + 3
\]

So, the slope-intercept form of the equation is:
\[
y = \frac{-9}{5}x + 3
\]

Would you like more details on any of the steps or have any questions?

### Related questions:
1. What is the significance of the slope in a linear equation?
2. How would you graph the line based on the slope-intercept form?
3. How can you convert slope-intercept form back to standard form?
4. What happens to the equation if you change the slope?
5. How can you find the x-intercept of this equation?

### Tip:
The slope \( m \) represents the rate of change in \( y \) with respect to \( x \). In this case, for every 5 units increase in \( x \), \( y \) decreases by 9 units.

Write the equation in slope-intercept form. 9x + 5y = 15

Learn how to convert the linear equation 9x + 5y = 15 into slope-intercept form (y = mx + b) with a detailed step-by-step solution. This exercise involves key algebraic concepts and is suitable for students in Grades 8-10.

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