Question

Given that the points (5,5) and (-5,1) are on a line, write an equation for that line in point-slope form.

Answer 1

To write the equation of the line in point-slope form, we'll first need to determine the slope of the line using the two given points: (5, 5) and (-5, 1).

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 (5, 5) as \((x_1, y_1)\) and (-5, 1) as \((x_2, y_2)\):

\[
m = \frac{1 - 5}{-5 - 5} = \frac{-4}{-10} = \frac{2}{5}
\]

Now that we have the slope \( m = \frac{2}{5} \), we can use the point-slope form of the equation of a line, which is:

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

We can choose either of the two given points. Let's use the point (5, 5).

Substituting \( m = \frac{2}{5} \), \( x_1 = 5 \), and \( y_1 = 5 \) into the point-slope form, we get:

\[
y - 5 = \frac{2}{5}(x - 5)
\]

This is the equation of the line in point-slope form.