Question

What is the equation written in point-slope form for a line that passes through (3, 6) and (1, 2)?
There are two possible answer choices.
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Answer 1

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:

1. \( y - 6 = 2(x - 3) \)
2. \( y - 2 = 2(x - 1) \)