A linear equation representing that Ben is five years younger than Luciana is y = x - 5. The provided choices do not accurately reflect this relationship, but understanding the formula y = a + bx, where a is the y-intercept and b is the slope, is essential.
Step-by-step explanation:
The question seeks to establish a linear equation that represents the age relationship between Ben and Luciana. Since Ben is five years younger than Luciana, this can be represented as y = x - 5, where x is Luciana's age and y is Ben's age. Thus, the correct equation to represent their age relationship would be y = x - 5.
In the provided choices, the equivalent choice is not listed directly, which suggests there might be a typo. However, understanding the concept of linear equations, which is in the form of y = a + bx (where a is the y-intercept and b is the slope), helps us determine that the relationship between the two ages involves subtraction because Ben is younger. Neither of the provided options accurately reflects this relationship, but the approach to identifying the correct relationship involves knowing that Ben's age is dependent on Luciana's and the difference is consistent at 5 years.