To find the equation of the line passing through the points $(1, 3)$ and $(2, 4)$, we can use the point-slope form of a line:

1. Find the slope ($m$): The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting in the points $(1, 3)$ and $(2, 4)$: $m = \frac{4 - 3}{2 - 1} = \frac{1}{1} = 1$

2. Use the point-slope form: The point-slope form of a line with slope $m$ passing through a point $(x_1, y_1)$ is: $y - y_1 = m(x - x_1)$ Using the point $(1, 3)$ and the slope $m = 1$: $y - 3 = 1(x - 1)$ Simplifying, we get: $y - 3 = x - 1$ $y = x + 2$

So, the equation of the line that passes through the points $(1, 3)$ and $(2, 4)$ is: $y = x + 2$

Would you like further details on the steps, or have any questions?

Here are some related questions to explore:

1. What is the equation of a line passing through points $(2, -1)$ and $(4, 3)$?
2. How do you find the equation of a line parallel to a given line through a specific point?
3. What is the process for finding the equation of a perpendicular line through a point?
4. How would you find the x-intercept and y-intercept of the line $y = x + 2$?
5. How does the point-slope form of a line compare to the slope-intercept form?

Tip: Remember, a line's slope indicates its "steepness" and direction. Positive slopes go up from left to right, while negative slopes go down.