https://file.aiquickdraw.com/mathbot/file/1727395095231hpec2ezn.jpg

Let's walk through the answers for the slope-intercept form questions on the worksheet.

### 1. **First Graph:**
The slope-intercept form is given by the equation:
\[
y = mx + b
\]
Where:
- \( m \) is the slope.
- \( b \) is the y-intercept.

#### From the graph:
- The slope (\(m\)) is the change in \(y\) divided by the change in \(x\) between two points on the line. Let's take two points from the graph: (0, 3) and (2, 0).
    - From (0, 3) to (2, 0), the change in \(y\) is \(0 - 3 = -3\), and the change in \(x\) is \(2 - 0 = 2\).
    - So, the slope \( m = \frac{-3}{2} = -\frac{3}{2} \).

- The y-intercept (\(b\)) is the point where the line crosses the y-axis. From the graph, it crosses at \( (0, 3) \), so \( b = 3 \).

- The x-intercept is the point where the line crosses the x-axis, which from the graph is \( (2, 0) \).

Thus, the equation of the line is:
\[
y = -\frac{3}{2}x + 3
\]

### 2. **Table:**
For each equation in the table, let's find the slope (\(m\)) and the y-intercept (\(b\)).

1. **\( y = 2x + 5 \)**:
   - Slope (\(m\)) = 2
   - Y-intercept (\(b\)) = 5

2. **\( y = -x - 3 \)**:
   - Slope (\(m\)) = -1 (since \( -x \) is equivalent to \( -1x \))
   - Y-intercept (\(b\)) = -3

3. **\( y = 7 \)**:
   - This is a horizontal line where \( y = 7 \) for all \(x\), so the slope (\(m\)) = 0.
   - Y-intercept (\(b\)) = 7

4. **\( y = -x \)**:
   - Slope (\(m\)) = -1
   - Y-intercept (\(b\)) = 0 (since no constant is added, \(b = 0\))

---

Let me know if you'd like any further details or clarifications.

### Follow-up questions:
1. How can you identify the slope from an equation in slope-intercept form?
2. What does the y-intercept tell you about a graph?
3. How do you determine the x-intercept from a graph?
4. What happens to the graph when the slope is positive versus negative?
5. Can you have a slope with a zero y-intercept? What would it look like?

### Tip:
To find the slope from a graph, always pick two clear points on the line and use the formula \( \text{slope} = \frac{\Delta y}{\Delta x} \).

Determine the slope and y-intercept from a graph and several linear equations.

Learn how to determine the slope and y-intercept from both a graph and linear equations. This problem involves the slope-intercept form of linear equations (y = mx + b) and calculating slope using coordinates. 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