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To find the equation of a line passing through the points (5,6) and (10,2), you can use the point-slope form of a linear equation:
\[y - y_1 = m(x - x_1)\]
Where:
- (x1, y1) is one of the points on the line, in this case, (5,6).
- m is the slope of the line.
First, calculate the slope (m):
\[m = \frac{y_2 - y_1}{x_2 - x_1}\]
Using (5,6) and (10,2):
\[m = \frac{2 - 6}{10 - 5} = \frac{-4}{5}\]
Now that you have the slope, you can use it in the point-slope form with one of the points (5,6):
\[y - 6 = \frac{-4}{5}(x - 5)\]
Now, you can simplify this equation:
\[y - 6 = \frac{-4}{5}x + 4\]
Add 6 to both sides of the equation to isolate y:
\[y = \frac{-4}{5}x + 10\]
So, the equation of the line passing through (5,6) and (10,2) is:
\[y = \frac{-4}{5}x + 10\]
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