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:

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