To derive the equation of the line that goes through the origin and the points (2, 10) and (1, 5), we can follow these steps:
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Find the slope (m): The slope (m) of a line that goes through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's use the points (2, 10) and (1, 5):
- \((x_1, y_1) = (1, 5)\)
- \((x_2, y_2) = (2, 10)\)
Plug in the values:
\[ m = \frac{10 - 5}{2 - 1} = \frac{5}{1} = 5 \]
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Write the equation of the line: Since we want the line through the origin (0, 0) with slope \(m\), the equation of the line can be expressed as:
\[ y = mx \]
Substituting the calculated slope:
\[ y = 5x \]
Therefore, the equation of the line passing through the origin with respect to the points given is:
\[ y = 5x \]
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