To find the equation of a line in point-slope form that passes through the points (3, 6) and (1, 2), we first need to calculate the slope of the line.
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (3, 6) and (1, 2):
- \( x_1 = 3 \), \( y_1 = 6 \)
- \( x_2 = 1 \), \( y_2 = 2 \)
Substituting these values into the slope formula, we get:
\[ m = \frac{2 - 6}{1 - 3} = \frac{-4}{-2} = 2 \]
Now that we have the slope \( m = 2 \), we can use point-slope form, which is given by:
\[ y - y_1 = m(x - x_1) \]
We can use either of the two points. Let's use the point (3, 6):
\[ y - 6 = 2(x - 3) \]
This is the equation of the line in point-slope form.
If you had to provide the alternative point (1, 2) instead, you would use:
\[ y - 2 = 2(x - 1) \]
Both forms are correct and represent the same line.
So, the two possible answers in point-slope form are:
- \( y - 6 = 2(x - 3) \)
- \( y - 2 = 2(x - 1) \)