https://file.aiquickdraw.com/mathbot/file/17263263968381eqyvmvc.jpg

The problem asks for the equation of the line, which follows the form \( y = mx \), where \( m \) is the slope of the line.

To find the slope \( m \), we can use two points from the table provided in the image: 
- \( (-4, -2) \)
- \( (0, 0) \)

The slope formula is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substitute the values from the two points \( (-4, -2) \) and \( (0, 0) \):

\[
m = \frac{0 - (-2)}{0 - (-4)} = \frac{2}{4} = \frac{1}{2}
\]

Thus, the equation of the line is:

\[
y = \frac{1}{2}x
\]

Would you like any additional details or have any questions about this? 

Here are 5 related questions to deepen your understanding:
1. How would the equation change if the line had a different slope?
2. How can you find the y-intercept of a line if it's not at the origin?
3. What happens to the slope if the line becomes steeper or less steep?
4. How would you calculate the slope if you had different points like \( (2, 1) \) and \( (4, 2) \)?
5. Can you use this method for vertical or horizontal lines, and if so, what would the equation look like?

**Tip:** When working with the slope formula, always pay attention to the sign of the differences in the coordinates to avoid errors in calculating the slope.

Write the equation of the line based on the graph and the table of points.

Learn how to write the equation of a line from a given set of points and graph. This example uses key concepts such as the slope formula and linear equations, suitable for students in Grades 7-9.

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