Question

A line passes through the points in this table.
x y
-4 -18
0 2
1 7
3 17
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 that passes through the points in the table, we can use the formula for the slope \( m \) between any two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Let's choose two points from the table, for example \((0, 2)\) and \((1, 7)\).

Here:
- \( (x_1, y_1) = (0, 2) \)
- \( (x_2, y_2) = (1, 7) \)

Now plug the values into the slope formula:

\[
m = \frac{7 - 2}{1 - 0} = \frac{5}{1} = 5
\]

To verify that this slope holds for other points in the table, we can check another pair, like \((1, 7)\) and \((3, 17)\).

Here:
- \( (x_1, y_1) = (1, 7) \)
- \( (x_2, y_2) = (3, 17) \)

So,

\[
m = \frac{17 - 7}{3 - 1} = \frac{10}{2} = 5
\]

Finally, let's verify with the points \((-4, -18)\) and \((0, 2)\):

Here:
- \( (x_1, y_1) = (-4, -18) \)
- \( (x_2, y_2) = (0, 2) \)

So,

\[
m = \frac{2 - (-18)}{0 - (-4)} = \frac{2 + 18}{0 + 4} = \frac{20}{4} = 5
\]

Since the slope is the same for all pairs of points we checked, we conclude that the slope of the line is:

\[
\boxed{5}
\]