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To find the equation of the line passing through the points \((-2, 3)\) and \((2, 5)\), we need to use the slope-intercept form of a linear equation, which is:

\[
y = mx + b
\]

Here, \(m\) is the slope, and \(b\) is the y-intercept.

### Step 1: Find the slope (\(m\))
The slope formula is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the points \((-2, 3)\) and \((2, 5)\):

\[
m = \frac{5 - 3}{2 - (-2)} = \frac{2}{4} = \frac{1}{2}
\]

### Step 2: Use the slope-intercept form
We now know that the slope is \(m = \frac{1}{2}\). Next, we use one of the points (let's use \((-2, 3)\)) to find the y-intercept \(b\). Substituting into the equation \(y = mx + b\):

\[
3 = \frac{1}{2}(-2) + b
\]

Simplifying:

\[
3 = -1 + b
\]

Solving for \(b\):

\[
b = 4
\]

### Step 3: Write the equation
Thus, the equation of the line is:

\[
y = \frac{1}{2}x + 4
\]

This is the equation of the line shown in the graph.

Do you have any questions, or would you like further explanation on any part of this?

Here are five related questions for further exploration:
1. How would the equation change if the slope were negative?
2. What is the significance of the y-intercept in a graph?
3. How can you find the equation if you are only given the slope and y-intercept?
4. Can you find the equation of a line parallel to this one passing through a different point?
5. What is the equation of a line perpendicular to this one?

**Tip:** Always simplify the slope to its lowest terms when calculating it between two points to avoid unnecessary complexity in the final equation.

Type an equation for the line shown in the graph, passing through points (-2, 3) and (2, 5).

Learn how to find the equation of a line passing through points (-2, 3) and (2, 5). This tutorial uses the slope-intercept form (y = mx + b) and explains how to calculate the slope and y-intercept step-by-step. Suitable for students in Grades 8-10.

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