what is the equation in point-slope form of the line that passes through the points (-4,2) and (12,6)?

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.

What is the equation in point-slope form of the line that passes through the points (-4,2) and (12,6)?

Learn how to find the equation in point-slope form for the line that passes through points (-4,2) and (12,6). This example covers key algebraic concepts, including calculating the slope and applying the point-slope formula. Suitable for students in Grades 8-10.

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