Without​ graphing, tell whether the slope of a line that models the linear relationship is​ positive, negative,​ zero, or undefined. Then find the slope.

Question

Upper A student earns a 95 on a test for answering one question incorrectly and earns a 85 for answering three questions incorrectly.
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Part 1
Choose the correct answer below.
A.
The slope of the relationship is zero.
B.
The slope of the relationship is positive.
C.
The slope of the relationship is negative.
D.
The slope of the relationship is undefined.

Answer 1

To analyze the relationship between the number of questions answered incorrectly and the corresponding score earned, we can look at the points given:

• When 1 question is answered incorrectly, the score is 95.
• When 3 questions are answered incorrectly, the score is 85.

We can represent these points as coordinates:

• Point A (1, 95)
• Point B (3, 85)

To find the slope (m) of the line that models this relationship, we use the slope formula:

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

Assigning our points:

• \( (x_1, y_1) = (1, 95) \)
• \( (x_2, y_2) = (3, 85) \)

Now we can substitute the values into the formula:

\[ m = \frac{85 - 95}{3 - 1} \] \[ m = \frac{-10}{2} = -5 \]

The slope is -5, which means that as the number of questions answered incorrectly increases, the score decreases.

Now, to answer your question:

C. The slope of the relationship is negative.