Bot GPT 4-o mini To find the equation of the line that passes through the origin (0,0) and has the same slope as the line described, we can follow these steps:
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Determine the slope (m): The slope of a line (m) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where (x1, y1) and (x2, y2) are two points on the line.
From the points (1, 4) and (2, 8):
- \( y_1 = 4, y_2 = 8, x_1 = 1, x_2 = 2 \)
Plugging in these values: \[ m = \frac{8 - 4}{2 - 1} = \frac{4}{1} = 4 \]
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Write the equation: The equation of a line that passes through the origin is given by: \[ y = mx \] Substituting the slope (m = 4): \[ y = 4x \]
Thus, the equation of the line through the origin that describes the proportional relationship shown in the graph is: \[ \boxed{y = 4x} \]
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