find the equation of a line through the following coordination. (5,6)and(10,2)

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: \[y = \frac{-4}{5}x + 10\]