Question

3.
Find the slope of the line that passes through the pair of points.

(1, 7), (10, 1)

Answer 1

To find the slope of the line that passes through the points \((1, 7)\) and \((10, 1)\), we can use the formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Here, the coordinates of the points are:
- \((x_1, y_1) = (1, 7)\)
- \((x_2, y_2) = (10, 1)\)

Now, we can substitute the values into the slope formula:

\[
m = \frac{1 - 7}{10 - 1}
\]

Calculating the values in the numerator and denominator:

\[
m = \frac{-6}{9}
\]

Now simplify the fraction:

\[
m = -\frac{2}{3}
\]

Thus, the slope of the line that passes through the points \((1, 7)\) and \((10, 1)\) is \(\boxed{-\frac{2}{3}}\).