express x as a function of y
Understand the Problem
The question is asking to rearrange an equation so that x is represented as a function of y. This typically involves algebraic manipulation to isolate x on one side of the equation.
Answer
$$ x(y) = \frac{y - 3}{2} $$
Answer for screen readers
$$ x(y) = \frac{y - 3}{2} $$
Steps to Solve
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Identify the equation
Start with the original equation given in the problem. If we have an equation like $y = 2x + 3$, this is where we begin. -
Isolate the term with x
Subtract the constant from both sides of the equation to move it away from the x term. For the example above, subtract 3: $$ y - 3 = 2x $$ -
Solve for x
Next, divide both sides of the equation by the coefficient of x to solve for x. In our case, the coefficient is 2: $$ x = \frac{y - 3}{2} $$ -
Rewrite as a function
Express x as a function of y. This can be written as: $$ x(y) = \frac{y - 3}{2} $$
$$ x(y) = \frac{y - 3}{2} $$
More Information
This shows that x is expressed as a function of y. The function allows us to find the value of x for any given value of y.
Tips
- Forgetting to perform the same operation on both sides of the equation, which can lead to incorrect answers. Always make sure to maintain equality.
- Not simplifying the equation correctly, which can result in a more complicated form rather than isolating x.
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