To find the y-intercept value, we need the equation of the line in the form:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

Step 1: Find the slope ($m$)

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute $(x_1, y_1) = (8, 3)$ and $(x_2, y_2) = (9, 4)$:

$m = \frac{4 - 3}{9 - 8} = \frac{1}{1} = 1$

Step 2: Use the point-slope form to find $b$

The point-slope form of the line equation is:

$y - y_1 = m(x - x_1)$

Substitute $m = 1$, $x_1 = 8$, and $y_1 = 3$:

$y - 3 = 1(x - 8)$

Simplify:

$y - 3 = x - 8$

$y = x - 8 + 3$

$y = x - 5$

Step 3: Identify the y-intercept ($b$)

In the equation $y = x - 5$, the y-intercept ($b$) is -5.

Final Answer:

The y-intercept value is:

$\boxed{-5}$

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Do you want further details or have any questions?
Here are 5 related questions for exploration:

1. How do you find the slope when given two points?
2. What is the general form of a line equation?
3. How can you verify the y-intercept on a graph?
4. What happens if the slope is zero or undefined?
5. How would the equation change if the points were flipped?

Tip: Always double-check your slope calculation to ensure accurate results!