The table shows ordered pairs of the function $y=8-2 x$. What is the value of $y$ when $x=8$ ?
$x$ | $y$ |
-3 | 14 |
-1 | 10 |
1 | 6 |
4 | 0 |
8 | ? |
10 | -12 |
The given function relating the variables \(x\) and \(y\) is \(y = 8 - 2x\). We are provided with a set of points in a table that satisfy this relationship, and we need to determine the value of \(y\) for the input \(x = 8\). This is a linear function, which can be graphed as a straight line. Each value of \(x\) corresponds to exactly one value of \(y\), which we can find by substitution.
To find the value of \(y\) when \(x = 8\), we substitute the value of \(x\) directly into the function formula:
\[y = 8 - 2(8)\]
Following the order of operations, we first multiply:
\[2 \times 8 = 16\]
Then, we subtract this from 8:
\[y = 8 - 16 = -8\]
Thus, the value of \(y\) when \(x = 8\) is \(-8\).
Linear functions are used in many real-life scenarios, such as budgeting. Suppose you have a total of \(\$8\) and you spend \(\$2\) for each game of mini-golf you play. The remaining amount of money \(y\) after \(x\) games would be modeled by the function \(y = 8 - 2x\). If you play 8 games, the function would tell you that you would have \(y = 8 - 2(8) = -8\), meaning you would owe money or need more funds to cover the cost. This basic algebraic model helps in predicting costs and managing resources efficiently.