https://file.aiquickdraw.com/mathbot/file/1727210470544xmgmnice.jpg

Let's solve the problems in the image step by step:

### Problem 3:
The graph shows a downward-sloping line. Let's calculate the **slope (m)** and **y-intercept (b)**:
1. **Slope (m)**: Use two points on the line. From the graph, we can see that the line passes through points \((0, 4)\) and \((2, 2)\).
   \[
   m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{2 - 4}}{{2 - 0}} = \frac{{-2}}{{2}} = -1
   \]
   So, the slope is \(m = -1\).

2. **y-intercept (b)**: The y-intercept is where the line crosses the y-axis, which is at \((0, 4)\). So, \(b = 4\).

### Problem 4:
This graph shows an upward-sloping line.
1. **Slope (m)**: Pick two points on the line, such as \((0, -3)\) and \((2, 1)\).
   \[
   m = \frac{{1 - (-3)}}{{2 - 0}} = \frac{4}{2} = 2
   \]
   So, the slope is \(m = 2\).

2. **y-intercept (b)**: The y-intercept is where the line crosses the y-axis, which is at \((0, -3)\). So, \(b = -3\).

### Problem 5 (Table):
The table provides points \((0, 3)\), \((5, 13)\), \((10, 23)\), \((15, 33)\), and \((20, 43)\).

1. **Slope (m)**: Use any two points, say \((0, 3)\) and \((5, 13)\).
   \[
   m = \frac{{13 - 3}}{{5 - 0}} = \frac{10}{5} = 2
   \]
   So, the slope is \(m = 2\).

2. **y-intercept (b)**: The y-intercept is when \(x = 0\), which is given as \(y = 3\). So, \(b = 3\).

### Problem 6 (Table):
The table provides points \((0, 5)\), \((2, 6)\), \((4, 7)\), \((6, 8)\), and \((8, 9)\).

1. **Slope (m)**: Use two points, say \((0, 5)\) and \((2, 6)\).
   \[
   m = \frac{{6 - 5}}{{2 - 0}} = \frac{1}{2}
   \]
   So, the slope is \(m = \frac{1}{2}\).

2. **y-intercept (b)**: The y-intercept is when \(x = 0\), which is given as \(y = 5\). So, \(b = 5\).

---

Let me know if you'd like more details or explanations for any of these problems! Here are five questions to extend your understanding:

1. What does the slope of a line tell you about its steepness and direction?
2. How does the y-intercept of a line affect where it crosses the y-axis?
3. If the slope of a line is zero, what type of line do you get?
4. How can you calculate the slope if you're only given a graph and no points?
5. How does the slope-intercept form of a line help in graphing linear equations?

**Tip**: To quickly check if points lie on a line, substitute the \(x\) and \(y\) values into the line equation \(y = mx + b\).

Find the slope and y-intercept of the lines represented by the graphs and tables.

Learn how to find the slope and y-intercept of linear equations using graphs and tables. This problem involves calculating the slope and identifying the y-intercept based on points, graphs, and tables. 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