https://file.aiquickdraw.com/mathbot/file/1728235453389c4vhd5mo.jpg

The slope is scaled by a factor of __ , and the y intercept is __

From the equation \( g(x) = 2(0.5x) + 3 \), we can analyze the scaling of the slope and the y-intercept:

1. **Simplify the equation**:
   \[
   g(x) = 2(0.5x) + 3 = (2 \times 0.5) x + 3 = x + 3
   \]
   So, the simplified equation is:
   \[
   g(x) = x + 3
   \]

2. **Slope scaling**:
   The original slope \( 0.5x \) has been scaled by a factor of 2 (due to multiplication by 2), so the slope is scaled by a factor of **2**.

3. **Y-intercept**:
   The y-intercept remains the constant value in the equation, which is **3**.

### Final Answer:
- The slope is scaled by a factor of **2**.
- The y-intercept is **3**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. What is the meaning of the slope in a linear function?
2. How would the graph of this function \( g(x) \) look compared to \( f(x) = 0.5x \)?
3. If the slope were scaled by 3 instead of 2, what would the equation look like?
4. How does the y-intercept affect the graph of a function?
5. What happens to the graph if we shift the entire function down by 4 units?

**Tip**: When scaling the slope in linear functions, the steepness of the graph changes, but the direction (positive or negative) is determined by the sign of the slope.

Analyze how the slope and y-intercept are affected in the equation g(x) = 2(0.5x) + 3. This detailed explanation simplifies the equation to g(x) = x + 3, demonstrating that the slope is scaled by a factor of 2, and the y-intercept is 3. Suitable for students in 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