To find the equation of the line in point-slope form that passes through the points $(-4, 2)$ and $(12, 6)$, follow these steps:

Step 1: Find the Slope

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

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

Using $(x_1, y_1) = (-4, 2)$ and $(x_2, y_2) = (12, 6)$:

$m = \frac{6 - 2}{12 - (-4)} = \frac{4}{16} = \frac{1}{4}$

So, the slope $m$ is $\frac{1}{4}$.

Step 2: Write the Equation in Point-Slope Form

The point-slope form of a line's equation is:

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

Using the point $(-4, 2)$ and the slope $m = \frac{1}{4}$:

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

Final Answer

The equation of the line in point-slope form is:

$\boxed{y - 2 = \frac{1}{4}(x + 4)}$

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Would you like further clarification on any part of this?

Here are 5 related questions for additional practice:

1. What is the equation of a line in point-slope form that passes through $(1, 3)$ with a slope of $2$?
2. How would you convert the point-slope form to slope-intercept form?
3. What is the slope of a line parallel to this line?
4. If a line passes through $(5, -1)$ with slope $-\frac{3}{5}$, what is its point-slope form?
5. How do you find the slope if only the x- and y-intercepts are given?

Tip: Point-slope form is particularly useful when you know the slope and any point on the line.