A line includes the points (1,6) and (10,3). What is its equation in point-slope form?

1 answer

To find the equation of the line in point-slope form, we first need to calculate the slope (m) of the line that passes through the points (1, 6) and (10, 3).

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Plugging in the coordinates of the points (1, 6) and (10, 3):

\[ m = \frac{3 - 6}{10 - 1} = \frac{-3}{9} = -\frac{1}{3} \]

Now that we have the slope, we can use the point-slope form of the equation of a line:

\[ y - y_1 = m(x - x_1) \]

Using the slope \( m = -\frac{1}{3} \) and one of the points, let's use (1, 6):

\[ y - 6 = -\frac{1}{3}(x - 1) \]

Thus, the equation of the line in point-slope form is:

\[ y - 6 = -\frac{1}{3}(x - 1) \]