Select the choice that represents this two-variable equation after it has been solved for $y$ in terms of $x$.
$3 y-x=1$
A. $y=\frac{x+1}{3}$
Answer (1)
Add x to both sides of the equation: 3 y = x + 1 .
Divide both sides of the equation by 3: y = 3 x + 1 .
The solution for y in terms of x is y = 3 x + 1 .
The final answer is y = 3 x + 1 .
Explanation
Understanding the Problem We are given the equation 3 y − x = 1 and asked to solve for y in terms of x . This means we want to isolate y on one side of the equation.
Adding x to both sides To isolate y , we first add x to both sides of the equation:
3 y − x + x = 1 + x
3 y = x + 1
Dividing by 3 Next, we divide both sides of the equation by 3:
3 3 y = 3 x + 1
y = 3 x + 1
Final Answer Therefore, the solution for y in terms of x is y = 3 x + 1 . Comparing this to the choices, we see that choice E matches our solution.
Examples
In physics, this type of equation can represent a relationship between two variables, such as the position and time of an object moving with constant acceleration. Solving for one variable in terms of the other allows us to predict the value of one variable if we know the value of the other. For example, if x represents time and y represents position, we can determine the position of the object at any given time using the equation y = 3 x + 1 .
