Question

Give that a line contains the points (10,15) and (15, 13), find the slope of that line using whatever method you want. Please describe in detail the method you used in complete sentences.

Answer 1

To find the slope of the line containing the points (10, 15) and (15, 13), we can use the formula for calculating the slope, which is defined as the change in the y-coordinates divided by the change in the x-coordinates of the two points.

The formula for slope \( m \) is given by:

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

Here, (x1, y1) can be taken as the first point (10, 15), and (x2, y2) can be taken as the second point (15, 13).

Now, we will substitute the values into the formula:

- For the first point (x1, y1), we have:
- x1 = 10
- y1 = 15

- For the second point (x2, y2), we have:
- x2 = 15
- y2 = 13

Now substituting these values into the formula gives:

\[
m = \frac{13 - 15}{15 - 10}
\]

Calculating the differences:

- \( y_2 - y_1 = 13 - 15 = -2 \)
- \( x_2 - x_1 = 15 - 10 = 5 \)

Putting these results back into the slope formula:

\[
m = \frac{-2}{5}
\]

Thus, the slope of the line connecting the points (10, 15) and (15, 13) is \( -\frac{2}{5} \).

In summary, the slope of the line was determined by using the slope formula, which involves calculating the difference between the y-coordinates divided by the difference between the x-coordinates of the two points provided. This resulted in a slope of \( -\frac{2}{5} \), indicating that the line descends as it moves from left to right.