Question

A line passes through the points (3,2) and (6,10). What is its equation in point-slope form?

Answer 1

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:

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