Which of the following expressions accurately describes the relationship $5x + 7y = 17$ as a function $y = f(x)$?
A. $y = f(x) = \frac{7}{17} - \frac{5}{7}x$
B. $y = f(x) = \frac{7}{17} - \frac{7}{5}x$
C. $y = f(x) = \frac{17}{7} - \frac{7}{5}x$
D. $y = f(x) = \frac{17}{7} - \frac{5}{7}x
Answer (1)
Subtract 5 x from both sides of the equation: 7 y = 17 − 5 x .
Divide both sides by 7: y = 7 17 − 5 x .
Rewrite the expression: y = 7 17 − 7 5 x .
The correct expression is: y = f ( x ) = 7 17 − 7 5 x .
Explanation
Understanding the Problem We are given the equation 5 x + 7 y = 17 and we want to express it in the form y = f ( x ) . This means we need to isolate y on one side of the equation.
Isolating the y term First, we subtract 5 x from both sides of the equation to get: 7 y = 17 − 5 x
Solving for y Next, we divide both sides of the equation by 7 to solve for y : y = f r a c 17 − 5 x 7
Rewriting the expression We can rewrite this expression as: y = 7 17 − 7 5 x
Identifying the correct option Now, we compare our derived expression y = 7 17 − 7 5 x with the given options. Option D, y = f ( x ) = 7 17 − 7 5 x , matches our result.
Final Answer Therefore, the correct expression is y = f ( x ) = 7 17 − 7 5 x .
Examples
In real-world scenarios, expressing a linear relationship as a function y = f ( x ) is useful for modeling how one variable depends on another. For example, if you have a budget of $17 and you spend $5 on each item x, the remaining money y can be expressed as a function of x. This allows you to easily calculate how much money you have left after buying a certain number of items, which is a practical application of rearranging linear equations.
