https://file.aiquickdraw.com/mathbot/file/1727191514552schqzxcr.jpg

The image shows a graph with the equation of a line passing through several points, including (-5, -5), (-2, -2), (3, 3), and (7, 7). To find the equation of the line, we can use the slope-intercept form of a linear equation:

\[
y = mx + b
\]

where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

### Step 1: Find the Slope \( m \)
The slope \( m \) is calculated as:

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

Using the points \((7,7)\) and \((3,3)\):

\[
m = \frac{7 - 3}{7 - 3} = \frac{4}{4} = 1
\]

Thus, the slope \( m = 1 \).

### Step 2: Find the y-intercept \( b \)
Now, substitute the slope \( m = 1 \) into the equation \( y = mx + b \), and use any point on the line to solve for \( b \). Let’s use the point \((3,3)\):

\[
3 = 1(3) + b
\]
\[
3 = 3 + b
\]
\[
b = 0
\]

### Final Equation
Thus, the equation of the line is:

\[
y = x
\]

This means the line has a slope of 1 and passes through the origin (0,0).

Would you like more details on any step, or do you have further questions?

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Here are 5 related questions to expand on this:
1. What happens if we choose different points to calculate the slope?
2. How can we verify that the line passes through the origin?
3. What does the slope of a line represent in general?
4. How would the equation change if the y-intercept were not 0?
5. How do we calculate the slope of a vertical or horizontal line?

**Tip:** Always verify the line’s slope by selecting two distinct points on the graph to ensure consistency.

Work out the equation of the line below using the points (-5, -5), (-2, -2), (3, 3), and (7, 7).

Learn how to find the equation of a line that passes through the points (-5, -5), (-2, -2), (3, 3), and (7, 7). This problem demonstrates how to calculate the slope and use the slope-intercept form to derive the equation. Suitable for students in Grades 8-10.

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