A line passes through the points (3,2) and (6,10). 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 determine the slope of the line that passes through the points (3, 2) and (6, 10).

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 \((3, 2)\) and \((6, 10)\), we can assign:

  • \( (x_1, y_1) = (3, 2) \)
  • \( (x_2, y_2) = (6, 10) \)

Now we can calculate the slope \( m \):

\[ m = \frac{10 - 2}{6 - 3} = \frac{8}{3} \]

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

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

We can use one of the points to write the equation. Let's use the point \((3, 2)\):

\[ y - 2 = \frac{8}{3}(x - 3) \]

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

\[ y - 2 = \frac{8}{3}(x - 3) \]