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To write the equation of a line in point-slope form, we first need to calculate the slope (\(m\)) using the two points provided: \((2, 3)\) and \((3, 7)\).

### Step 1: Calculate the slope (\(m\))
The slope formula 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:
\[
m = \frac{7 - 3}{3 - 2} = \frac{4}{1} = 4
\]

### Step 2: Use the point-slope formula
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]

We can use either of the given points. Let's use \((2, 3)\):
\[
y - 3 = 4(x - 2)
\]

This is the equation of the line in point-slope form.

Would you like further details on solving this, or any additional clarifications?

Here are some related questions to expand your understanding:
1. How do you convert the point-slope form to slope-intercept form?
2. What would the equation look like if you used the point \((3, 7)\) instead?
3. Can you use the point-slope form to find the equation of a line perpendicular to this one?
4. How would you determine if a third point lies on this line?
5. What is the significance of the slope value in this line's equation?

**Tip:** When working with two points, always ensure you compute the slope first, as this defines the steepness and direction of the line.

Write an equation of the line in point-slope form that passes through the given points (2,3) and (3,7).

Learn how to find the equation of a line in point-slope form that passes through two points, (2,3) and (3,7). This problem covers key algebraic concepts like slope calculation and the point-slope formula, making it suitable for students in Grades 8-10.

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