Question

a high school football team scores a total of 42 points by scoring touchdowns and field goals. suppose each field goal is worth 3 points, and each touchdown is worth 7 points complete parts a and b

a. let x represent the number of field goals and y represent the number of touchdowns. write an equation that models the total points scored in the game. choose the correct answer.

◯ a. 42x + 7y = 3
◯ b. 3x + 7y = 42
◯ c. 7x + 3y = 42
◯ d. 3x + 42y = 7

b. identify and interpret the x - and y - intercepts.

the x - intercept is □, which means that the team scored □. the y - intercept is □, which means that the team scored □
(type whole numbers.)

Explanation:

Step1: Determine the equation for part a

The total points from field goals is \(3x\) (since each field goal \(x\) is worth 3 points) and the total points from touchdowns is \(7y\) (since each touchdown \(y\) is worth 7 points). The total points scored is 42. So the equation is \(3x + 7y=42\).

Step2: Find the \(x\) - intercept for part b

To find the \(x\) - intercept, set \(y = 0\).

$$
LATEXBLOCK0
$$

This means the team scored 14 field goals and 0 touchdowns.

Step3: Find the \(y\) - intercept for part b

To find the \(y\) - intercept, set \(x = 0\).

$$
LATEXBLOCK1
$$

This means the team scored 6 touchdowns and 0 field goals.

Answer:

a. B. \(3x + 7y = 42\)
b. The \(x\) - intercept is \(14\), which means that the team scored 14 field goals and 0 touchdowns. The \(y\) - intercept is \(6\), which means that the team scored 6 touchdowns and 0 field goals.