Question

find point slope form of 5,7 and -1,3

Answer 1

To find the point-slope form of the equation of a line that passes through the points \((5, 7)\) and \((-1, 3)\), we first need to find the slope \(m\) of the line.

The formula for finding 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 \((5, 7)\) and \((-1, 3)\), we can assign:

\[
(x_1, y_1) = (5, 7) \quad \text{and} \quad (x_2, y_2) = (-1, 3)
\]

Now, substituting these values into the slope formula:

\[
m = \frac{3 - 7}{-1 - 5} = \frac{-4}{-6} = \frac{2}{3}
\]

Now that we have the slope \(m = \frac{2}{3}\), 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 either of the two points; let's use \((5, 7)\):

\[
y - 7 = \frac{2}{3}(x - 5)
\]

This is the point-slope form of the equation of the line that passes through the points \((5, 7)\) and \((-1, 3)\). If you want it in a different format or if you have any more questions, feel free to ask!