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.