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The image shows a question that asks to find the equation of a line through two points, \( (2, 1) \) and \( (3, 4) \), in slope-intercept form.

Let's go step by step to solve it:

1. **Find the slope of the line** using the slope formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   where \( (x_1, y_1) = (2, 1) \) and \( (x_2, y_2) = (3, 4) \).

2. **Substitute** the values into the formula:
   \[
   m = \frac{4 - 1}{3 - 2} = \frac{3}{1} = 3
   \]
   So, the slope \( m = 3 \).

3. **Use the point-slope form** of the equation of a line:
   \[
   y - y_1 = m(x - x_1)
   \]
   Using point \( (2, 1) \), the equation becomes:
   \[
   y - 1 = 3(x - 2)
   \]

4. **Simplify** the equation:
   \[
   y - 1 = 3x - 6
   \]
   Add 1 to both sides:
   \[
   y = 3x - 5
   \]

Thus, the equation of the line is:
\[
y = 3x - 5
\]

Would you like any further details or clarifications?

Here are 5 related questions for practice:
1. How do you find the equation of a line given a point and the slope?
2. What is the point-slope form of a line, and when is it used?
3. Can a line have the same slope but pass through different points? What does that represent geometrically?
4. How do you convert point-slope form to slope-intercept form?
5. How can you determine the x- and y-intercepts of the line \( y = 3x - 5 \)?

**Tip**: Always check your calculations, especially when determining the slope, to avoid simple mistakes in line equations.

Find the equation of the line in terms of y = mx + b that passes through the points (2, 1) and (3, 4).

Learn how to find the equation of a line in slope-intercept form, passing through the points (2, 1) and (3, 4). This step-by-step solution explains how to calculate the slope and form the equation y = 3x - 5, perfect for Grades 8-10.

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