To write the equation of the line that passes through the points (5,5) and (-5,1) in point-slope form, we first need to determine the slope of the line using these two points.
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's assign the points as follows:
- \((x_1, y_1) = (5, 5)\)
- \((x_2, y_2) = (-5, 1)\)
Now, we can plug these values into the slope formula:
\[ m = \frac{1 - 5}{-5 - 5} = \frac{-4}{-10} = \frac{2}{5} \]
Now that we have the slope \( m = \frac{2}{5} \), we can use the point-slope form of the equation for a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
We can use either of the given points to write the equation. Let's use the point (5, 5).
Substituting \( m = \frac{2}{5} \), and \( (x_1, y_1) = (5, 5) \) into the point-slope form:
\[ y - 5 = \frac{2}{5}(x - 5) \]
Thus, the equation of the line in point-slope form is:
\[ y - 5 = \frac{2}{5}(x - 5) \]
In conclusion, to find the equation, I calculated the slope between the two points using the slope formula, and then used that slope in the point-slope form equation with one of the points.
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