Let's go through each question step by step.
(Questions part A)
To find the slope \( M \) of a line passing through points \((x_{1}, y_{1})\) and \((x_{2}, y_{2})\), the formula for slope is:
\[ M = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \]
So, filling in the blanks:
- blank 1: \(y_{2}\) (D)
- blank 2: \(y_{1}\) (C)
- blank 3: \(x_{2}\) (A)
- blank 4: \(x_{1}\) (B)
Thus, the answer is:
\[ M = \frac{D - C}{A - B} \]
(Questions part B)
Now, we calculate the slope \( M \) using the points (1, 1) and (3, 5). Specifically, let:
- \( (x_{1}, y_{1}) = (1, 1) \)
- \( (x_{2}, y_{2}) = (3, 5) \)
Plugging in these values:
\[ M = \frac{5 - 1}{3 - 1} = \frac{4}{2} = 2 \]
Filling in the blanks:
- blank 1: \(5\) (A)
- blank 2: \(1\) (C)
- blank 3: \(3\) (B)
- blank 4: \(1\) (A)
So, the answer is:
\[ M = \frac{A - C}{B - A} = \frac{5 - 1}{3 - 1} = 2 \]
(Questions part C)
We already established that \(M = 2\). Now we need to follow the format given:
Using \(M = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
Filling in:
- blank 1: \(4\) (C)
- blank 2: \(2\) (B)
Thus, the answer for blank 3 is \(2\) (B).
In summary:
-
For part A:
- M = \frac{D - C}{A - B}
-
For part B:
- M = 2
-
For part C:
- M = \frac{C}{B}
- Answer: 2
1 answer