https://file.aiquickdraw.com/mathbot/file/1725430515771dgpgrmfe.jpg

The function provided in the image is \( f(x) = \frac{1}{2}x - 7 \).

This is a linear function in the form \( f(x) = mx + b \), where:
- \( m = \frac{1}{2} \) is the slope of the line,
- \( b = -7 \) is the y-intercept, which is the point where the line crosses the y-axis.

### Key Properties of the Function:
1. **Slope (\(m\))**: The slope is \( \frac{1}{2} \), meaning for every 1 unit increase in \( x \), \( f(x) \) increases by \( \frac{1}{2} \) units.
2. **Y-intercept (\(b\))**: The y-intercept is -7, so the line crosses the y-axis at the point (0, -7).
3. **X-intercept**: To find the x-intercept, set \( f(x) = 0 \) and solve for \( x \):
   \[
   0 = \frac{1}{2}x - 7
   \]
   \[
   \frac{1}{2}x = 7
   \]
   \[
   x = 14
   \]
   So, the line crosses the x-axis at the point (14, 0).

Would you like more details on any specific aspect or have any questions?

### Related Questions:
1. How would you graph the function \( f(x) = \frac{1}{2}x - 7 \) on the coordinate plane?
2. What is the meaning of the slope and y-intercept in a real-world context?
3. How does changing the slope \( \frac{1}{2} \) affect the graph of the function?
4. How would you find the point of intersection between this line and another line, say \( g(x) = -x + 3 \)?
5. What is the range of the function \( f(x) = \frac{1}{2}x - 7 \)?

### Tip:
When graphing a linear equation, it's helpful to identify the y-intercept and another point on the line (like the x-intercept) to draw the line accurately.

What is the function represented by the equation f(x) = 1/2 x - 7?

Explore the linear function f(x) = 1/2x - 7. This problem delves into key algebraic concepts, including the slope-intercept form, and helps students understand how to find the slope, y-intercept, and x-intercept. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation