Question

Write and equation in point slope form that passes through 2,-7 and 6,-3

Answer 1

To write the equation in point-slope form, we first need to determine the slope (m) using the two points given: \( (2, -7) \) and \( (6, -3) \).

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

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

Substituting in the coordinates of the points:

- \( x_1 = 2 \), \( y_1 = -7 \)
- \( x_2 = 6 \), \( y_2 = -3 \)

We get:

\[
m = \frac{-3 - (-7)}{6 - 2} = \frac{-3 + 7}{4} = \frac{4}{4} = 1
\]

Now that we have the slope \( m = 1 \), we can use one of the points to write the equation in point-slope form. We'll use the point \( (2, -7) \).

The point-slope form of a line is given by the equation:

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

Substituting in our slope and the point \( (2, -7) \):

\[
y - (-7) = 1(x - 2)
\]

Simplifying this, we have:

\[
y + 7 = 1(x - 2)
\]

This can be further simplified to:

\[
y + 7 = x - 2
\]

Thus, the point-slope form of the equation that passes through the points \( (2, -7) \) and \( (6, -3) \) is:

\[
y + 7 = 1(x - 2)
\]