To find the equation of the line passing through the points $(2, 4)$ and $(6, 10)$, we'll use the slope-intercept form of a line, which is:

$y = mx + b$

Step 1: Find the slope $m$

The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the points $(2, 4)$ and $(6, 10)$:

$m = \frac{10 - 4}{6 - 2} = \frac{6}{4} = \frac{3}{2}$

Step 2: Use the point-slope form to find the equation

We can now use the point-slope form of the equation of a line:

$y - y_1 = m(x - x_1)$

Using the point $(2, 4)$ and the slope $m = \frac{3}{2}$:

$y - 4 = \frac{3}{2}(x - 2)$

Step 3: Simplify the equation

Distribute the slope on the right-hand side:

$y - 4 = \frac{3}{2}x - 3$

Add 4 to both sides to solve for $y$:

$y = \frac{3}{2}x - 3 + 4$ $y = \frac{3}{2}x + 1$

Final equation

The equation of the line is:

$y = \frac{3}{2}x + 1$

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How can we verify if another point lies on this line?
2. What is the significance of the slope in this equation?
3. How would the equation change if we use a different set of points?
4. How can we convert this equation to standard form?
5. What does the y-intercept represent in this context?

Tip: The slope of a line tells you how steep the line is. A positive slope indicates the line rises as you move from left to right.