Question

A line passes through the points in this table.
x y
-17 -18
-7 -2
3 14
13 30
What is the slope of the line?
Write your answer as an integer or simplified fraction.

Answer 1

To find the slope of the line passing through the given points, we can use any two points from the table to calculate the slope. The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Let's calculate the slope using the first two points (-17, -18) and (-7, -2).

Here, \((x_1, y_1) = (-17, -18)\) and \((x_2, y_2) = (-7, -2)\).

Calculating the differences:

\[
y_2 - y_1 = -2 - (-18) = -2 + 18 = 16
\]
\[
x_2 - x_1 = -7 - (-17) = -7 + 17 = 10
\]

Now, substitute the differences into the slope formula:

\[
m = \frac{16}{10} = \frac{8}{5}
\]

Now, to confirm that the slope remains consistent with the other points, we can calculate using the second and third points (-7, -2) and (3, 14).

Here, \((x_1, y_1) = (-7, -2)\) and \((x_2, y_2) = (3, 14)\).

Calculating:

\[
y_2 - y_1 = 14 - (-2) = 14 + 2 = 16
\]
\[
x_2 - x_1 = 3 - (-7) = 3 + 7 = 10
\]

Again, substituting into the slope formula:

\[
m = \frac{16}{10} = \frac{8}{5}
\]

Finally, we can check the slope using the third and fourth points (3, 14) and (13, 30).

Here, \((x_1, y_1) = (3, 14)\) and \((x_2, y_2) = (13, 30)\).

Calculating:

\[
y_2 - y_1 = 30 - 14 = 16
\]
\[
x_2 - x_1 = 13 - 3 = 10
\]

Substituting into the slope formula:

\[
m = \frac{16}{10} = \frac{8}{5}
\]

Since the slope calculated with all pairs of points is consistent, we conclude that the slope of the line is:

\[
\boxed{\frac{8}{5}}
\]