The graph of a linear function f is shown. a. Identify the slope, y-intercept, and x-intercept. b. Write the equation that defines f. Ay 10- The slope is 6- (Type an integer or a simplified fraction.) 4- 2- to -8 64 10 -4 -8 10-
The graph of a linear function f is shown. a. Identify the slope, y-intercept, and x-intercept. b. Write the equation that defines f. Ay 10- The slope is 6- (Type an integer or a simplified fraction.) 4- 2- to -8 64 10 -4 -8 10-
Transcribed Image Text:### Educational Content on Linear Functions
#### The Graph of a Linear Function
The graph of a linear function \( f \) is shown below.
##### Tasks:
1. **Identify the slope, y-intercept, and x-intercept.**
2. **Write the equation that defines \( f \).**
**Identifying Key Features:**
- The slope is \( \boxed{-1} \).
*(Type an integer or a simplified fraction.)*
**Graph Explanation:**
The graph displayed is a Cartesian coordinate plane with both x and y axes ranging from -10 to 10. The linear function graph is a straight line that intersects the y-axis at \( y = 8 \) and the x-axis at \( x = 8 \).
**Steps to Identify:**
1. **Slope (m):**
- The slope of a line is calculated using the formula \( \frac{\Delta y}{\Delta x} \).
- On the graph, the line goes down by 8 units vertically (change in \( y \)) for every 8 units it moves horizontally (change in \( x \)), giving a slope of \( \frac{-8}{8} = -1 \).
2. **Y-intercept (b):**
- The y-intercept is the point where the line crosses the y-axis. On this graph, the y-intercept is at \( y = 8 \).
3. **X-intercept:**
- The x-intercept is the point where the line crosses the x-axis. On this graph, the x-intercept is at \( x = 8 \).
**Writing the Equation of the Line:**
- For a linear function in the form \( y = mx + b \):
- Given the slope \( m = -1 \) and the y-intercept \( b = 8 \),
- The equation defining \( f \) is \( y = -x + 8 \).
By understanding these key elements, students can better grasp the properties and equations of linear functions.
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