Question

a professional quarterback throws a football for an average of 65 yards plus or minus 5 yards. if y is the distance the ball is thrown in yards, write an equation representing the maximum and minimum yards thrown on average.
| y - 65 | = 5
| y + 65 | = 5
| y + 5 | = 65
| y - 5 | = 65

Explanation:

Step1: Understand Absolute Value Concept

The absolute value equation \(|x - a| = b\) (where \(b\geq0\)) represents that \(x\) is at a distance \(b\) from \(a\) on the number line. So \(x=a + b\) or \(x=a - b\). Here, the average (center) is 65 yards, and the deviation is 5 yards. Let \(y\) be the distance thrown. The difference between \(y\) and 65 should be 5 (since it's plus or minus 5 from 65). So the equation is \(|y - 65|=5\).

Step2: Analyze Other Options

• For \(|y + 65| = 5\), this would mean \(y\) is 5 units from - 65, which doesn't match the context (average is 65, not - 65).
• For \(|y+5| = 65\), this implies \(y\) is 65 units from - 5, not related to the average of 65.
• For \(|y - 5| = 65\), this implies \(y\) is 65 units from 5, not related to the average of 65.

Answer:

\(|y - 65| = 5\) (the first option: \(|y - 65| = 5\))