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The problem asks to find the equation of the line passing through the points \((0, 5)\) and \((4, 6)\).

We can use the point-slope form of a line equation, which is written as:

\[
y = mx + b
\]

Where:
- \(m\) is the slope
- \(b\) is the y-intercept.

### Step 1: Find 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 points \((0, 5)\) and \((4, 6)\):

\[
m = \frac{6 - 5}{4 - 0} = \frac{1}{4}
\]

### Step 2: Find the y-intercept \(b\)
To find \(b\), substitute one of the points (preferably \((0, 5)\)) into the equation \(y = mx + b\).

Using the point \((0, 5)\):

\[
5 = \frac{1}{4}(0) + b
\]

So, \(b = 5\).

### Final equation
Thus, the equation of the line is:

\[
y = \frac{1}{4}x + 5
\]

Would you like any further details or clarification?

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Here are some related questions:
1. How do you derive the slope-intercept form from other forms of linear equations?
2. What does the slope represent geometrically?
3. How can we graph the line \(y = \frac{1}{4}x + 5\) on a coordinate plane?
4. How would the equation change if the line passed through different points?
5. How do you calculate the slope when the points are vertical or horizontal?

**Tip:** Always double-check the slope calculation by ensuring the correct subtraction of coordinates.

The equation for a line through the two points (0, 5) and (4, 6) is y = ___x + ___

Learn how to find the equation of a line passing through the points (0, 5) and (4, 6). This solution explains how to calculate the slope and determine the y-intercept using algebraic concepts and the slope-intercept form y = mx + b. Suitable for students in Grades 8-10.

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