https://file.aiquickdraw.com/mathbot/file/1724116771075bh2hfz5s.jpg

Use the graph of the line below to find the equation of the line.

To find the equation of the line shown in the graph, we'll follow a similar process as before:

### 1. **Identify Two Points on the Line:**
   From the image, it looks like the line passes through:
   - Point \( A = (-3, -5) \)
   - Point \( B = (3, 5) \)

### 2. **Calculate the Slope (m):**
   The slope \( m \) of the line is calculated using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Substituting the coordinates of points \( A \) and \( B \):
   \[
   m = \frac{5 - (-5)}{3 - (-3)} = \frac{5 + 5}{3 + 3} = \frac{10}{6} = \frac{5}{3}
   \]

### 3. **Use the Point-Slope Form to Find the Equation:**
   The point-slope form of the line equation is:
   \[
   y - y_1 = m(x - x_1)
   \]
   Using point \( A(-3, -5) \) and slope \( m = \frac{5}{3} \):
   \[
   y + 5 = \frac{5}{3}(x + 3)
   \]
   Simplifying:
   \[
   y + 5 = \frac{5}{3}x + 5
   \]
   \[
   y = \frac{5}{3}x
   \]

Therefore, the equation of the line is:

\[
y = \frac{5}{3}x
\]

Would you like more details or have any further questions?

Here are 5 related questions to expand on this:

1. How would the equation change if the slope were negative?
2. What is the equation of a line perpendicular to this one?
3. How do you find the x-intercept from the equation of the line?
4. Can this equation be converted into standard form? If so, how?
5. How can you determine the equation of a line given only its slope and one point on the line?

**Tip:** When graphing or reading the equation of a line, always double-check the slope's sign by noting the direction the line moves from left to right.

Discover how to find the equation of a line from its graph. Step-by-step solution using points on the line and slope calculation. Suitable for students in Grades 7-9.

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