To determine which ordered pair forms a proportional relationship with the point (0, 0) and the point (45, 30), we first need to find the slope of the line that passes through these two points.
The slope \( m \) can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates of the points (45, 30) (which is \( (x_2, y_2) \)) and (0, 0) (which is \( (x_1, y_1) \)):
\[ m = \frac{30 - 0}{45 - 0} = \frac{30}{45} = \frac{2}{3} \]
A proportional relationship can be represented by the equation \( y = kx \), where \( k \) is the constant of proportionality. In this case, the constant \( k \) corresponds to the slope we calculated, which is \( \frac{2}{3} \). Therefore, any point \( (x, y) \) that maintains this ratio \( \frac{y}{x} = \frac{2}{3} \) will form a proportional relationship.
To check each of the ordered pairs given:
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For \( (10, 10) \): \[ \frac{10}{10} = 1 \quad \text{(not proportional)} \]
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For \( (25, 35) \): \[ \frac{35}{25} = 1.4 \quad \text{(not proportional)} \]
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For \( (70, 50) \): \[ \frac{50}{70} = \frac{5}{7} \quad \text{(not proportional)} \]
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For \( (90, 60) \): \[ \frac{60}{90} = \frac{2}{3} \quad \text{(this is proportional)} \]
The only ordered pair that forms a proportional relationship with the line through the points (0, 0) and (45, 30) is (90, 60).