A) The equation for the slope \( m \) of a line that passes through two points \((x_{1}, y_{1})\) and \((x_{2}, y_{2})\) is given by:
\[ m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \]
B) To find the slope of a linear function containing the points (1, 1) and (3, 5):
Using the points:
- \( (x_{1}, y_{1}) = (1, 1) \)
- \( (x_{2}, y_{2}) = (3, 5) \)
Substituting into the slope formula: \[ m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{5 - 1}{3 - 1} \]
Top part:
- blank 1 = 5 (which is \( y_{2} \))
- blank 2 = 1 (which is \( y_{1} \))
Bottom part:
- blank 3 = 3 (which is \( x_{2} \))
- blank 4 = 1 (which is \( x_{1} \))
Thus, the slope \( m \) is calculated as follows:
\[ m = \frac{5 - 1}{3 - 1} = \frac{4}{2} = 2 \]
Therefore, the answers for the blanks are:
- blank 1 = 5
- blank 2 = 1
- blank 3 = 3
- blank 4 = 1
So the slope \( m \) is equal to 2.
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