Question

josue is taking a multiple choice test. his grade is given by the equation $y = 100 - 5x$, where $y$ represents his final score and $x$ represents the number of questions he got wrong. what could the number 5 represent in the equation?
answer
his score with 0 problems wrong.
the score he would get if he only missed one question.
the change in his score for every one problem he got wrong.
the number of problems on the test.

Explanation:

1. Analyze the first option: "His score with 0 problems wrong" would be when \( x = 0 \), substituting into \( y=100 - 5x \), we get \( y = 100-5\times0=100 \). So this represents the score when \( x = 0 \), not related to the number 5.
2. Analyze the second option: The equation is in the form of a linear equation \( y=mx + b \), where \( m \) is the slope (rate of change). Here, the equation is \( y=100-5x \), which can be written as \( y=- 5x + 100 \). The coefficient of \( x \) (which is - 5, and the magnitude 5 here) represents the rate of change of \( y \) with respect to \( x \). Since \( x \) is the number of questions wrong, 5 (or - 5) represents how much the score \( y \) changes for each unit change in \( x \) (each question wrong). So this option "The change in his score for every one problem he got wrong" matches the meaning of the coefficient 5.
3. Analyze the third option: If he only missed one question, \( x = 1 \), then \( y=100 - 5\times1=95 \). This is the score when \( x = 1 \), not what 5 represents.
4. Analyze the fourth option: The number of problems on the test is not represented by 5. The total score when \( x = 0 \) is 100, but that's not the number of problems.

Answer:

The change in his score for every one problem he got wrong.