https://file.aiquickdraw.com/mathbot/file/1724427550977duey0765.jpg

To write the equation of the line shown in the image, we need to determine its slope and y-intercept.

1. **Identify two points on the line**: From the graph, we can see two points that the line passes through:
   - Point 1: \((2, -1)\)
   - Point 2: \((6, 3)\)

2. **Calculate the slope** (\(m\)):
   The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting the values from the points:
   \[
   m = \frac{3 - (-1)}{6 - 2} = \frac{4}{4} = 1
   \]

3. **Find the y-intercept** (\(b\)): 
   The y-intercept is the value of \(y\) when \(x = 0\). We can use the slope-intercept form of the equation \(y = mx + b\). Using one of the points \((2, -1)\):
   \[
   -1 = 1(2) + b \implies -1 = 2 + b \implies b = -3
   \]

4. **Write the equation**: 
   The equation of the line in slope-intercept form \(y = mx + b\) is:
   \[
   y = x - 3
   \]

This is the equation of the line shown in the image.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How would the equation change if the slope was steeper?
2. What is the general form of a line equation and how does it relate to the slope-intercept form?
3. Can you find the equation of a line parallel to the given line?
4. How would you find the equation of a line perpendicular to the given line?
5. What happens to the y-intercept if you shift the line up or down?

**Tip:** Always start by identifying key points on a graph to help find the slope and y-intercept when writing the equation of a line.

Learn how to write the equation of a line using slope and y-intercept. This detailed explanation covers identifying points on the graph, calculating the slope, finding the y-intercept, and writing the equation in slope-intercept form. Suitable for students in Grades 7-9.

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