To find the slope of Arabella's line, which is perpendicular to the line shown in the graph, we need to determine the slope of the given line first. Then, we use the fact that the slopes of two perpendicular lines are negative reciprocals of each other.

Step 1: Determine the slope of the given line

From the graph, the line appears to pass through the points $(0, 7)$ and $(7, 0)$. We can use these points to calculate the slope of the line using the slope formula:

$\text{slope of given line} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 7}{7 - 0} = \frac{-7}{7} = -1$

Step 2: Find the slope of the perpendicular line

The slope of Arabella's line, being perpendicular to the given line, will be the negative reciprocal of $-1$. The negative reciprocal of $-1$ is:

$\text{slope of Arabella's line} = \frac{1}{-1} = 1$

Step 3: Match the slope with the given options

However, none of the options directly show "1." Let’s recheck the provided answers:

• $7$
• $4$
• $\frac{4}{7}$
• $-\frac{7}{4}$

Since the graph's scale or some other aspects might suggest something different, the correct approach here relies on rechecking specific visual points. Yet, based on usual geometry rules, for perpendicularity if one line's slope is negative ($-7/4$), perpendicular ones lead to options with an