Select the equation that is equivalent to [tex]$4 x-2 y=3$[/tex].
Answer (1)
Isolate y in the given equation 4 x − 2 y = 3 .
Rewrite the equation in the form y = f ( x ) .
Simplify the equation.
The equivalent equation is y = 2 x − 2 3 .
Explanation
Understanding the Problem We are given the equation 4 x − 2 y = 3 and we want to find an equivalent equation.
Isolating y To find an equivalent equation, we can isolate y in the given equation. Start by subtracting 4 x from both sides: − 2 y = − 4 x + 3
Dividing by -2 Next, divide both sides by − 2 : y = − 2 − 4 x + 3
Simplifying Simplify the equation: y = − 2 − 4 x + − 2 3 y = 2 x − 2 3
Final Answer Therefore, the equation equivalent to 4 x − 2 y = 3 is y = 2 x − 2 3 .
Examples
Understanding equivalent equations is crucial in many real-world scenarios. For example, when converting between temperature scales like Celsius and Fahrenheit, you're essentially using equivalent equations to express the same temperature in different units. Similarly, in physics, different equations might describe the same physical phenomenon under different conditions, and being able to recognize their equivalence helps in problem-solving.
