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The problem asks to find the equation of the line passing through the points \((2, 4)\) and \((6, 10)\).

We can solve this using the point-slope form of a line equation:
\[
y - y_1 = m(x - x_1)
\]
where \(m\) is the slope, and \((x_1, y_1)\) is one of the points.

### Step 1: Calculate the slope
The slope \(m\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 4}{6 - 2} = \frac{6}{4} = 1.5
\]

### Step 2: Use the point-slope form
Now we can use one of the points, say \((2, 4)\), to write the equation:
\[
y - 4 = 1.5(x - 2)
\]

### Step 3: Simplify to slope-intercept form
Expanding the equation:
\[
y - 4 = 1.5x - 3
\]
\[
y = 1.5x - 3 + 4
\]
\[
y = 1.5x + 1
\]

Thus, the equation of the line is:
\[
y = 1.5x + 1
\]

Would you like more details or further explanations?

Here are five related questions you can explore:
1. What is the slope-intercept form of a line?
2. How do you derive the point-slope form of a line equation?
3. What happens if the two points are vertical?
4. Can you find the equation of a line if given the slope and a point?
5. How does the slope indicate if a line is increasing or decreasing?

**Tip**: Always check the slope first when writing the equation of a line—it tells you the steepness and direction.

Find the equation of the line passing through the points (2, 4) and (6, 10).

Learn how to find the equation of a line passing through the points (2, 4) and (6, 10). This problem explores key concepts in algebra and coordinate geometry, such as the slope formula, point-slope form, and slope-intercept form. Suitable for students in Grades 8-10.

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