The problem asks us to find the equation of a line in the form $y = mx + b$, given that the line 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 $y = mx + b$, given that the line 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 formula is:

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

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:

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

So, the slope $m$ is $\frac{3}{4}$.

Now we have the equation $y = \frac{3}{4}x + b$.

To find the y-intercept $b$, we can substitute one of the given points into the equation. Let's use the point $(4, 1)$.

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

$1 = 3 + b$

$b = 1 - 3$

$b = -2$

So, the y-intercept $b$ is $-2$.

Now we can write the equation of the line as $y = \frac{3}{4}x - 2$.

3. Final Answer

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