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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

Arabella wants to make a line perpendicular to the line given. What is the slope of Arabella's line?

Learn how to determine the slope of a line perpendicular to a given line. This problem involves calculating the slope using the slope formula and understanding the concept of negative reciprocals for perpendicular slopes. Suitable for students in Grades 8-10.

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