To write the equation of a line in point-slope form, we first need to determine the slope $m$ of the line passing through the two given points $(2, 4)$ and $(4, 8)$.

Step 1: Calculate the Slope

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 given points:

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

Step 2: Write the Point-Slope Form

The point-slope form of a line is given by:

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

Using the slope $m = 2$ and the point $(2, 4)$, the point-slope form of the equation is:

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

Step 3: Simplify to Slope-Intercept Form

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

$y - 4 = 2x - 4$

Adding 4 to both sides:

$y = 2x$

So, the slope-intercept form of the equation is:

$y = 2x$

Summary:

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

Would you like any more details or have any questions?

Here are some related questions you might consider:

1. How do you find the midpoint between two points?
2. How do you convert the point-slope form to the standard form of a line?
3. What is the geometric interpretation of the slope in a linear equation?
4. How do you determine if two lines are parallel?
5. What is the relationship between the slopes of perpendicular lines?

Tip: Always double-check your calculations when determining the slope, as it affects the entire equation.