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The equation given is \( y = -3x + 9 \). This equation is in the slope-intercept form \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept of the line.

### 1. Rate of Change (Slope)
The rate of change, or slope, is the coefficient of \( x \). Here, it is \( m = -3 \). This means for every unit increase in \( x \), \( y \) decreases by 3 units.

### 2. y-Intercept
The y-intercept is the value of \( y \) when \( x = 0 \). This can be directly read off from the equation as \( b = 9 \). So, the y-intercept is \( y = 9 \).

### 3. x-Intercept
The x-intercept occurs where \( y = 0 \). To find it, set \( y \) to 0 and solve for \( x \):

\[ 0 = -3x + 9 \]
\[ -3x = -9 \]
\[ x = 3 \]

Thus, the x-intercept is \( x = 3 \).

Therefore:
- Rate of change (slope) is \(-3\).
- y-intercept is \( y = 9 \).
- x-intercept is \( x = 3 \).

Would you like more details on this or have any questions? Here are a few follow-up questions:
1. Would you like to see a graph of this line?
2. How does the sign of the slope affect the direction of the line?
3. Can you explain why the x-intercept occurs at \( x = 3 \)?
4. What would happen to the graph if the slope were positive instead?
5. How would changing the y-intercept affect the position of the graph?

**Tip:** Remember, in the equation \( y = mx + b \), altering \( m \) changes the steepness and direction of the line, while altering \( b \) shifts the line up or down without changing its slope.

Identify the key features of the line y = -3x + 9. (Work required.)

Learn how to identify the key features of the linear equation y = -3x + 9. This step-by-step solution explains how to determine the slope, x-intercept, and y-intercept. Suitable for students in Grades 8-10.

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