Question

What is the slope of the line passing through the points (6, 5) and (3, 1)? Show and explain simple work

Answer 1

To find the slope of the line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we can use the formula for slope \(m\):

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

In our case, we have the points \((6, 5)\) and \((3, 1)\). We assign the coordinates as follows:

- \((x_1, y_1) = (6, 5)\)
- \((x_2, y_2) = (3, 1)\)

Now we can substitute these values into the formula:

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

Calculating the numerator and the denominator:

\[
m = \frac{-4}{-3}
\]

Now, simplifying the fraction:

\[
m = \frac{4}{3}
\]

Thus, the slope of the line passing through the points \((6, 5)\) and \((3, 1)\) is \( \frac{4}{3} \).