Question

The points (6,
–
2) and (5,
–
5) fall on a particular line. What is its equation in point-slope form?

Answer 1

To find the equation of the line that passes through the points \((6, -2)\) and \((5, -5)\) in point-slope form, 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:

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

Substituting the coordinates of the points \((6, -2)\) and \((5, -5)\):

- \(x_1 = 6\), \(y_1 = -2\)
- \(x_2 = 5\), \(y_2 = -5\)

Now, we compute the slope:

\[
m = \frac{-5 - (-2)}{5 - 6} = \frac{-5 + 2}{5 - 6} = \frac{-3}{-1} = 3
\]

Now that we have the slope \(m = 3\), we can use one of the points to write the equation in point-slope form. The point-slope form of the equation of a line is given by:

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

Using the point \((6, -2)\) and the slope \(m = 3\):

\[
y - (-2) = 3(x - 6)
\]

This simplifies to:

\[
y + 2 = 3(x - 6)
\]

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

\[
y + 2 = 3(x - 6)
\]