The problem asks us to find the slope and y-intercept of the line shown in the graph and then write the equation of the line.

1. Problem Description

The problem asks us to find the slope and y-intercept of the line shown in the graph and then write the equation of the line.

2. Solution Steps

First, let's identify two points on the line from the graph. From the graph, we can see the line passes through the points $(0, 4)$ and $(2, 7)$.

The slope $m$ of the line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

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

Using the points $(0, 4)$ and $(2, 7)$, we have:

$m = \frac{7 - 4}{2 - 0} = \frac{3}{2}$

The y-intercept is the point where the line crosses the y-axis, which is the y-coordinate when $x = 0$. From the graph, we can directly read the y-intercept as $4$. Therefore, $b = 4$.

The slope-intercept form of a linear equation is:

$y = mx + b$

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

Substituting the values of $m$ and $b$, we get:

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

The question asks for the slope only.

3. Final Answer

$\frac{3}{2}$