To find the equation of the line in point-slope form, we first need to determine the slope of the line that passes through the points (2, –5) and (5, –6).
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \((2, -5)\) and \((5, -6)\):
- Let \((x_1, y_1) = (2, -5)\)
- Let \((x_2, y_2) = (5, -6)\)
Now, plug these values into the slope formula:
\[ m = \frac{-6 - (-5)}{5 - 2} = \frac{-6 + 5}{5 - 2} = \frac{-1}{3} \]
Thus, the slope \( m \) is \(-\frac{1}{3}\).
Next, we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
We can choose either of the two points to use in this formula. Let's use the point (2, -5):
- \( (x_1, y_1) = (2, -5) \)
- \( m = -\frac{1}{3} \)
Substituting these values into the point-slope form, we get:
\[ y - (-5) = -\frac{1}{3}(x - 2) \]
This simplifies to:
\[ y + 5 = -\frac{1}{3}(x - 2) \]
So, the equation of the line in point-slope form is:
\[ y + 5 = -\frac{1}{3}(x - 2) \]