Given the points $(2, 4)$ and $(4, 8)$, let's write the equation of the line in point-slope form and then convert it to slope-intercept form.

Step 1: Find the Slope

The slope $m$ is calculated using the formula:

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

Substituting the points $(x_1, y_1) = (2, 4)$ and $(x_2, y_2) = (4, 8)$:

$m = \frac{8 - 4}{4 - 2} = \frac{4}{2} = 2$

Step 2: Write the Point-Slope Form

The point-slope form of a line is:

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

Using the slope $m = 2$ and the point $(2, 4)$:

$y - 4 = 2(x - 2)$

Step 3: Simplify to Slope-Intercept Form

To convert this to slope-intercept form ($y = mx + b$), expand and simplify:

$y - 4 = 2x - 4$

Add 4 to both sides:

$y = 2x$

Final Answer:

• Point-Slope Form: $y - 4 = 2(x - 2)$
• Slope-Intercept Form: $y = 2x$

If you need more details or have questions, feel free to ask!

Here are some related questions you might consider:

1. How can you verify if a point lies on the line given its equation?
2. What is the equation of a line parallel to this one passing through a different point?
3. How would the equation change if one of the points was negative?
4. How do you find the y-intercept directly from two points?
5. What is the equation of the line perpendicular to this one passing through $(2, 4)$?

Tip: When working with fractions or more complex numbers, it's often useful to check your work by substituting the points back into the equation to ensure they satisfy it.