https://file.aiquickdraw.com/mathbot/file/1729601254631qg7pnd2s.jpg

Let's analyze the problem from your uploaded image. The question involves the linear equation:

\[
y = 7.5x + 2
\]

### Standard Form Analysis:
The equation is in **slope-intercept form**:  
\[
y = mx + b
\]
where:
- \(m\) is the **slope**.
- \(b\) is the **y-intercept**.

From the given equation:
- **Slope \(m\)** = 7.5
- **y-intercept \(b\)** = 2

### Now let's evaluate the given statements:

1. **The slope is 2.**  
   - **Incorrect.** The slope is 7.5, not 2.

2. **The slope is 7.5.**  
   - **Correct.** This matches the slope from the equation.

3. **The y-intercept is 2.**  
   - **Correct.** This matches the \(b\)-value.

4. **The y-intercept is 7.5.**  
   - **Incorrect.** The y-intercept is 2, not 7.5.

5. **The rate of change is less than 1.**  
   - **Incorrect.** The slope of 7.5 indicates a steep positive change, which is greater than 1.

6. **The rate of change is greater than 1.**  
   - **Correct.** Since the slope is 7.5, the rate of change is indeed greater than 1.

---

### Correct Selections:
- The slope is 7.5.
- The y-intercept is 2.
- The rate of change is greater than 1.

Do you need more clarification or further explanation?

---

Here are 5 follow-up questions for deeper understanding:
1. What does the slope tell us about the behavior of a graph?
2. How do you identify the y-intercept from an equation?
3. What happens to the graph if the slope is negative?
4. How would the graph change if the y-intercept were negative?
5. How can we calculate the slope from two points on the graph?

**Tip:** The larger the slope, the steeper the graph. If it's greater than 1, the line rises quickly.

Select all of the statements that are true about the graph of y = 7.5x + 2.

Analyze the linear equation y = 7.5x + 2 by identifying its slope and y-intercept. Learn to distinguish between correct and incorrect statements about the slope, y-intercept, and rate of change. 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