Question

an 84 - point test has x questions worth 4 points and y questions worth 3 points. write an equation in standard form that describes all possible numbers of questions that may be on the test. what is the y - intercept and what does the y - intercept mean? a. the y - intercept is (0, 28) and it means there are 28 questions worth 3 points each and no 4 - point questions. b. the y - intercept is (0, 21) and it means there are 21 questions worth 3 points each and no 4 - point questions. c. the y - intercept is (28, 0) and it means there are 28 questions worth 4 points each and no 3 - point questions. d. the y - intercept is (21, 0) and it means there are 21 questions worth 4 points each and no 3 - point questions.

Explanation:

Step1: Establecer la ecuación

La puntuación total de la prueba es 84 puntos. Las preguntas de 4 puntos son $x$ y las de 3 puntos son $y$. Entonces, la ecuación en forma estándar es $4x + 3y=84$.

Step2: Encontrar el intercepto - y

Para encontrar el intercepto - y, se hace $x = 0$. Sustituyendo $x = 0$ en la ecuación $4x+3y = 84$, obtenemos $3y=84$, entonces $y = 28$. El intercepto - y es el punto $(0,28)$. Esto significa que cuando no hay preguntas de 4 puntos ($x = 0$), hay 28 preguntas de 3 puntos.

Answer:

C. The y - intercept is $(0,28)$ and it means there are 28 questions worth 3 points and no 4 - point questions.