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

Upper A student earns a 95 on a test for answering one question incorrectly and earns a 85 for answering three questions incorrectly.
Question content area bottom
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.
Your answer is correct.D.
The slope of the relationship is undefined.
Part 2
Find the slope. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The slope is
  
enter your response here.​ (Simplify your​ answer.)

1 answer

To determine the slope of the line that models the relationship between the number of questions answered incorrectly and the test score, we can observe the provided data:

  1. The student earns a score of 95 for answering one question incorrectly.
  2. The student earns a score of 85 for answering three questions incorrectly.

From this information, we can derive two points for our linear relationship:

  • Point 1: (1, 95) - where 1 is the number of incorrect answers and 95 is the score.
  • Point 2: (3, 85) - where 3 is the number of incorrect answers and 85 is the score.

Part 1: Determine the slope

The slope of a line (m) can be calculated using the formula:

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

Where:

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

Substituting these coordinates into the formula gives:

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

Since the slope is negative, the correct answer for Part 1 is: C. The slope of the relationship is negative.

Part 2: Find the slope

From the calculation above, we found that:

A. The slope is -5.

So, the completed choices are: C. The slope of the relationship is negative. A. The slope is -5.