The problem asks us to find the equation of a line in the form $y = mx + b$ that passes through the points $(4, 1)$ and $(8, 4)$.

1. Problem Description

The problem asks us to find the equation of a line in the form $y = mx + b$ that passes through the points $(4, 1)$ and $(8, 4)$.

2. Solution Steps

First, we need to find the slope $m$ of the line. The slope is given by the formula:

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

Using the given points $(4, 1)$ and $(8, 4)$, we have $x_1 = 4$, $y_1 = 1$, $x_2 = 8$, and $y_2 = 4$. Plugging these values into the slope formula, we get:

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

Now that we have the slope $m = \frac{3}{4}$, we can plug this into the equation $y = mx + b$, so we have:

$y = \frac{3}{4}x + b$

Next, we need to find the y-intercept $b$. We can use one of the given points to solve for $b$. Let's use the point $(4, 1)$. Substituting $x = 4$ and $y = 1$ into the equation, we get:

$1 = \frac{3}{4}(4) + b$

$1 = 3 + b$

Subtracting 3 from both sides, we get:

$b = 1 - 3 = -2$

So, the equation of the line is $y = \frac{3}{4}x - 2$.

3. Final Answer

$y = \frac{3}{4}x - 2$