Question

1. football tyrell plays running back and kicks field goals for his team. he scores 6 points for a touchdown and 3 points for a field goal. in his last game, he scored 24 points. this can be represented by the function 6x + 3y = 24. find the x - and y - intercepts. interpret the x - and y - intercepts.

Explanation:

Step1: Find the x - intercept

The x - intercept occurs when \(y = 0\).
Substitute \(y = 0\) into \(6x+3y = 24\):
\(6x+3\times0=24\)
\(6x=24\)
\(x=\frac{24}{6}=4\)

Step2: Find the y - intercept

The y - intercept occurs when \(x = 0\).
Substitute \(x = 0\) into \(6x + 3y=24\):
\(6\times0+3y=24\)
\(3y=24\)
\(y=\frac{24}{3}=8\)

Step3: Interpret the intercepts

For the x - intercept \((4,0)\): If Tyrell scores \(0\) field goals (\(y = 0\)), he scores \(4\) touchdowns (\(x = 4\)).
For the y - intercept \((0,8)\): If Tyrell scores \(0\) touchdowns (\(x = 0\)), he scores \(8\) field goals (\(y = 8\)).

Answer:

The x - intercept is \(4\) and the y - intercept is \(8\). The x - intercept \((4,0)\) means if there are \(0\) field goals, there are \(4\) touchdowns. The y - intercept \((0,8)\) means if there are \(0\) touchdowns, there are \(8\) field goals.