Question

A line passes through the points (9, 30) and (18, 30). Which statement is true about the line?
It has a slope of zero because the change in the y-values is 0.
It has no slope because the change in the y-values is 0.
It has a slope of zero because the change in the x-values is 0.
It has no slope because the change in the x-values is 0.

Answer 1

To determine the nature of the line that passes through the points (9, 30) and (18, 30), we first calculate the slope of the line.

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Using the points provided:

- \((x_1, y_1) = (9, 30)\)
- \((x_2, y_2) = (18, 30)\)

We can substitute the values into the slope formula:

\[
m = \frac{30 - 30}{18 - 9} = \frac{0}{9} = 0
\]

Since the slope \( m = 0 \), this indicates that the line is horizontal.

Now, let's analyze the given statements:

1. **It has a slope of zero because the change in the y-values is 0.** - This is true. The change in y-values is indeed 0 (30 - 30 = 0), leading to a slope of 0.

2. **It has no slope because the change in the y-values is 0.** - This is misleading. A slope of 0 does signify that the line is horizontal, but we typically would say it has a slope of zero, not that it has "no slope."

3. **It has a slope of zero because the change in the x-values is 0.** - This is incorrect. The change in the x-values is not 0 (18 - 9 = 9); rather, the change in y-values is what gives us a slope of 0.

4. **It has no slope because the change in the x-values is 0.** - This is incorrect for the same reason as above; the change in x-values is not 0.

Thus, the correct statement is:

**It has a slope of zero because the change in the y-values is 0.**