To adjust the equation of the line so that it passes through the points (5, 2.3) and (2, 10), you will first need to find the slope of the line that connects these two points and then use one of the points to write the new equation.
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Find the slope (m): The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (5, 2.3) and (2, 10):
- \(x_1 = 5\), \(y_1 = 2.3\)
- \(x_2 = 2\), \(y_2 = 10\)
\[ m = \frac{10 - 2.3}{2 - 5} = \frac{7.7}{-3} \approx -2.5667 \]
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Use the point-slope form: Once you have the slope, you can use the point-slope form of a line to write the new equation. The point-slope form is:
\[ y - y_1 = m(x - x_1) \]
Let's use point (5, 2.3):
\[ y - 2.3 = -2.5667(x - 5) \]
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Expand and simplify:
\[ y - 2.3 = -2.5667x + 12.8335 \]
\[ y = -2.5667x + 12.8335 + 2.3 \]
\[ y = -2.5667x + 15.1335 \]
So the new equation of the line that passes through the points (5, 2.3) and (2, 10) is approximately:
\[ y \approx -2.5667x + 15.1335 \]
If you wish for it to be more simplified, you can round the values, but that is the general equation that correctly passes through the two points.
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