Question

What is a simple way to tell that

is not the slope of this graph?


On a coordinate plane, a line goes through points A (0, 2.5) and B (0.833, 0).
Clear Check

The
-intercept is

, not

.



The line slants downward, so the slope is negative.



A slope cannot be a mixed number.



The change in
from
to
is negative.

Answer 1

To determine whether a value represents the slope of the line defined by points A (0, 2.5) and B (0.833, 0), we need to calculate the slope using the formula:

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

Here, \( (x_1, y_1) = (0, 2.5) \) and \( (x_2, y_2) = (0.833, 0) \). Plugging the coordinates into the formula:

\[
\text{slope} = \frac{0 - 2.5}{0.833 - 0} = \frac{-2.5}{0.833}
\]

Calculating that value gives a negative result, confirming that the slope of the line is indeed negative.

Now let's go through the statements provided:

1. **The y-intercept is not - (missing value)**: This statement is only about the y-intercept and does not directly pertain to the slope.

2. **The line slants downward, so the slope is negative**: This statement is true and confirms that the slope is negative.

3. **A slope cannot be a mixed number**: This statement is incorrect; slopes can indeed be expressed as mixed numbers.

4. **The change in y from A to B is negative**: This is a factual statement about the points, indicating that the line decreases from A to B, which is consistent with a negative slope.

A clear and simple way to conclude that a given value is not the slope of this graph is the statement **"The line slants downward, so the slope is negative,"** if the slope provided is positive (or zero), indicating that it does not match the actual slope calculated from points A and B. If the indicated slope value is positive or zero, it's not correct.