Question

Use the graph below for all parts of question 5.



Part 1

Find the slope of the line between points A and C. (Do not reduce the fraction.)

m =
Question 2
Part 2

Find the slope of the line between points C and E.

m =
Question 3
Part 3



The slope between points A & C, and C & E are
Choose...
fractions. The similar triangles they form prove that no matter what
Choose...
points are picked on the line the slope will be
Choose...
.

Answer 1

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
1. Identify the coordinates of points A and C. Let's assume \(A(x_1, y_1)\) and \(C(x_2, y_2)\).
2. Use the slope formula:
\[
m_{AC} = \frac{y_C - y_A}{x_C - x_A}
\]
3. Substitute the actual values you have for coordinates A and C to find \(m_{AC}\).

### Part 2: Slope between Points C and E
1. Identify the coordinates of points C and E. Let's assume \(C(x_1, y_1)\) and \(E(x_2, y_2)\).
2. Use the slope formula:
\[
m_{CE} = \frac{y_E - y_C}{x_E - x_C}
\]
3. 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!