To find the slopes between the specified points, we need the coordinates for points A, C, and E. Assuming the points are given by their coordinates (x1, y1) and (x2, y2), the formula for calculating the slope \( m \) between two points is:
\[ m = \frac{y2 - y1}{x2 - x1} \]
Part 1: Slope of the Line between Points A and C
Let's denote the coordinates of point A as \((x_A, y_A)\) and point C as \((x_C, y_C)\).
The slope \( m \) between points A and C is:
\[ m = \frac{y_C - y_A}{x_C - x_A} \]
Part 2: Slope of the Line between Points C and E
Let the coordinates of point E be \((x_E, y_E)\).
The slope \( m \) between points C and E is:
\[ m = \frac{y_E - y_C}{x_E - x_C} \]
Part 3: Conclusion on Slopes
Both slopes found in parts 1 and 2 will yield fractions. The similar triangles they form along the line illustrate that regardless of the specific points selected along the line, the slopes will remain consistent.
To provide exact slope values, please provide the coordinates for points A, C, and E from the graph mentioned.
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