The problem requires us to find the equation of a line given a point $P_0(0, 4)$ and the slope $m = \frac{3}{4}$.

1. Problem Description

The problem requires us to find the equation of a line given a point $P_0(0, 4)$ and the slope $m = \frac{3}{4}$.

2. Solution Steps

We will use the point-slope form of a linear equation, which is:

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

where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line.

In this case, we have $x_1 = 0$, $y_1 = 4$, and $m = \frac{3}{4}$. Substituting these values into the point-slope form gives:

$y - 4 = \frac{3}{4}(x - 0)$

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

To get the equation in slope-intercept form, we solve for $y$:

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

3. Final Answer

The equation of the line is $y = \frac{3}{4}x + 4$.