https://file.aiquickdraw.com/mathbot/file/1727395192522x78cblui.jpg

Let's break down and work through this worksheet.

### Part 1: Information Based on the Graph
The first part of the worksheet asks for the slope, y-intercept, and the equation of the line from the given graph. Here’s how we analyze it:

1. **Finding the slope**:
   The line on the graph slopes downward, meaning the slope (\(m\)) is negative. We can calculate the slope using two points on the line. From the graph, we see:
   - The line passes through the point (0, 4) (the y-intercept) and another point like (2, 0) (x-intercept).
   - Slope \(m = \frac{\text{rise}}{\text{run}} = \frac{4 - 0}{0 - 2} = -2\).

   So, the slope \(m = -2\).

2. **The y-intercept**:
   The y-intercept (\(b\)) is the point where the line crosses the y-axis. From the graph, this is at the point (0, 4), so \(b = 4\).

3. **The x-intercept**:
   The x-intercept is the point where the line crosses the x-axis. From the graph, this is at the point (2, 0), so the x-intercept is 2.

4. **Equation of the line**:
   Using the slope-intercept form \(y = mx + b\), where \(m = -2\) and \(b = 4\), the equation of the line is:
   \[
   y = -2x + 4
   \]

### Part 2: Determining the Slope and Y-Intercept from the Equations

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

2. **Equation: \(y = -x - 3\)**
   - Slope (\(m\)) = -1 (since the coefficient of \(x\) is -1)
   - Y-intercept (\(b\)) = -3

3. **Equation: \(y = 7\)**
   - This is a horizontal line, so the slope (\(m\)) is 0 (because there's no \(x\)-term).
   - Y-intercept (\(b\)) = 7

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

---

### Summary:

#### Part 1 (From the graph):
- Slope (\(m\)): \(-2\)
- Y-intercept (\(b\)): \(4\)
- X-intercept: \(2\)
- Equation: \(y = -2x + 4\)

#### Part 2 (From the equations):
1. \(y = 2x + 5\): \(m = 2\), \(b = 5\)
2. \(y = -x - 3\): \(m = -1\), \(b = -3\)
3. \(y = 7\): \(m = 0\), \(b = 7\)
4. \(y = -x\): \(m = -1\), \(b = 0\)

---

Would you like further details on any of these steps, or do you have any questions? Here are some related questions:

1. What does a positive slope indicate about the direction of a line?
2. How does the y-intercept affect the position of a line on a graph?
3. What is the difference between slope-intercept form and point-slope form?
4. How can you determine the x-intercept of a line if you know the equation?
5. How do horizontal lines differ in their equations compared to vertical lines?

**Tip:** When identifying the slope from a graph, always pick two points and apply the formula \( \frac{\text{rise}}{\text{run}} \).

Analyzing a worksheet on slope-intercept form, finding the slope, y-intercept, x-intercept, and the equation from a given graph, and determining slope and y-intercept from provided equations.

Learn how to find the slope, y-intercept, and equation of a line using the slope-intercept form. Analyze a graph and determine key points, as well as identify the slope and y-intercept from various linear equations. Suitable for Grade 8 Algebra students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation