https://file.aiquickdraw.com/mathbot/file/1727096428251rmzbl6t5.jpg

Let's analyze the graph and answer the questions:

### a. What is the y-intercept?
The y-intercept is the point where the line crosses the y-axis. In the graph, the line crosses the y-axis at \( (0, 5) \). Therefore, the **y-intercept is 5**.

### b. What is the slope?
To find the slope, we use the formula:
\[
\text{slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 5) \) and \( (6, 1) \):
\[
\text{slope} = \frac{1 - 5}{6 - 0} = \frac{-4}{6} = -\frac{2}{3}
\]
So, the **slope is \( -\frac{2}{3} \)**.

### c. What is the equation of the line in slope-intercept form?
The slope-intercept form of a line is given by:
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the y-intercept. From the previous steps, we know the slope \( m = -\frac{2}{3} \) and the y-intercept \( b = 5 \). So, the equation of the line is:
\[
y = -\frac{2}{3}x + 5
\]

### d. Is this a proportional or non-proportional relationship?
A proportional relationship is a line that passes through the origin \( (0, 0) \). Since the line passes through \( (0, 5) \), it does not go through the origin, making it a **non-proportional** relationship.

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Would you like more details on any of the steps? Here are 5 questions to extend your learning:

1. How would the equation of the line change if the y-intercept were 0?
2. What is the meaning of a negative slope in a real-world scenario?
3. How can you verify if two points lie on the same line using the slope?
4. How would the graph look if the slope were positive but the same magnitude \( \frac{2}{3} \)?
5. What is the relationship between the slope and the angle of inclination of the line?

**Tip:** The slope determines the steepness and direction of a line—negative slopes go downwards from left to right, while positive slopes go upwards.

Look at the graph and answer the following questions:
 a) What is the y-intercept?
 b) What is the slope?
 c) What is the equation of the line in slope-intercept form?
 d) Is this a proportional or non-proportional relationship?

This problem involves analyzing a linear graph to determine the y-intercept, slope, and writing the equation in slope-intercept form. It also checks if the relationship is proportional. Suitable for middle school students in Grades 6-8.

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