To find the slope-intercept form of the line that passes through the points $(1, 2)$ and $(3, 6)$, follow these steps:

1. Calculate the slope (m): The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

   Plugging in the given points $(1, 2)$ and $(3, 6)$: $m = \frac{6 - 2}{3 - 1} = \frac{4}{2} = 2$

   So, the slope $m$ is 2.

2. Use the point-slope form of the line equation: The general equation of a line in point-slope form is: $y - y_1 = m(x - x_1)$ Using point $(1, 2)$ and slope $m = 2$: $y - 2 = 2(x - 1)$

3. Convert to slope-intercept form (y = mx + b): Expand and simplify the equation: $y - 2 = 2x - 2$ $y = 2x$

   Therefore, the slope-intercept form of the line is: $y = 2x$

Would you like a further breakdown of the steps, or do you have any questions?

Additional Related Questions

1. How do you find the slope of a line given two points?
2. What is the point-slope form, and when is it useful?
3. Can you convert a line from point-slope to slope-intercept form in any situation?
4. How do you find the y-intercept when only given two points?
5. What is the general form of a line equation, and how does it differ from the slope-intercept form?

Tip:

Always check that the slope calculation is accurate, as small mistakes in slope can change the entire equation of the line.