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?

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.