Select the choice that represents this two-variable equation after it has been solved for $y$ in terms of $x$.
$2 y=8 x+4$
Answer (2)
Divide both sides of the equation by 2: 2 2 y = 2 8 x + 4 .
Simplify the equation: y = 2 8 x + 2 4 .
Perform the division: y = 4 x + 2 .
The equation solved for y in terms of x is: y = 4 x + 2 .
Explanation
Understanding the Problem We are given the equation 2 y = 8 x + 4 and we want to solve for y in terms of x . This means we want to isolate y on one side of the equation.
Dividing Both Sides by 2 To isolate y , we need to divide both sides of the equation by 2: 2 2 y = 2 8 x + 4
Simplifying the Equation Now, we simplify the equation by dividing each term on the right side by 2: y = 2 8 x + 2 4
Final Solution Performing the division, we get: y = 4 x + 2
Examples
In real life, this type of equation can represent a simple linear relationship between two variables. For example, if x represents the number of hours worked and y represents the total earnings, the equation y = 4 x + 2 could mean that you earn $4 per hour plus a fixed bonus of 2. S o l v in g f or y$ allows you to easily calculate your total earnings based on the number of hours worked.
The equation 2 y = 8 x + 4 can be solved for y in terms of x by dividing both sides by 2, leading to y = 4 x + 2 . Therefore, the final answer is y = 4 x + 2 .
;
