The problem asks us to graph the function $f(x) = \frac{3}{4}x + 5$. This is a linear function in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. Problem Description

The problem asks us to graph the function $f(x) = \frac{3}{4}x + 5$. This is a linear function in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

2. Solution Steps

First, we identify the slope and y-intercept of the function. The given function is $f(x) = \frac{3}{4}x + 5$. Comparing this with the slope-intercept form $y = mx + b$, we have:

$m = \frac{3}{4}$ (slope)

$b = 5$ (y-intercept)

The y-intercept is the point where the line crosses the y-axis, which is $(0, 5)$. We can use the slope to find another point on the line. The slope $\frac{3}{4}$ means that for every 4 units we move to the right along the x-axis, we move 3 units up along the y-axis. Starting from the y-intercept $(0, 5)$, if we move 4 units to the right (i.e., $x=4$), the y-value will increase by 3, so we have:

$y = \frac{3}{4}(4) + 5 = 3 + 5 = 8$

So, the point $(4, 8)$ is also on the line. We can graph the line using the points $(0, 5)$ and $(4, 8)$.

3. Final Answer

The graph of the function $f(x) = \frac{3}{4}x + 5$ is a straight line passing through the points $(0, 5)$ and $(4, 8)$.