To solve the questions, we need to calculate the slope (m) of the lines represented by the points A, C, and E. The slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
However, since I cannot see the graph or actual coordinates of points A, C, and E, I'll provide the general steps for you to follow to calculate the slope.
Part 1: Slope between Points A and C
- Identify the coordinates of points A and C. Let's assume \(A(x_1, y_1)\) and \(C(x_2, y_2)\).
- Use the slope formula: \[ m_{AC} = \frac{y_C - y_A}{x_C - x_A} \]
- Substitute the actual values you have for coordinates A and C to find \(m_{AC}\).
Part 2: Slope between Points C and E
- Identify the coordinates of points C and E. Let's assume \(C(x_1, y_1)\) and \(E(x_2, y_2)\).
- Use the slope formula: \[ m_{CE} = \frac{y_E - y_C}{x_E - x_C} \]
- Substitute the actual values you have for coordinates C and E to find \(m_{CE}\).
Part 3: Choosing Appropriate Terms
After you have found both slopes (assuming both calculations lead to fractions):
- The slopes between points A & C, and C & E are fractions.
- The similar triangles they form prove that no matter what points are picked on the line, the slope will be the same.
Now you can plug in the actual calculations you made for specific values for points A, C, and E, and use the suggested filler words to complete the sentences!
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