Solve the formula $-4 x+y=-6$ for $y$.
Answer (1)
We are given the equation − 4 x + y = − 6 .
Add 4 x to both sides of the equation to isolate y : − 4 x + y + 4 x = − 6 + 4 x .
Simplify the equation: y = 4 x − 6 .
The solution for y is y = 4 x − 6 .
Explanation
Understanding the Problem We are given the equation − 4 x + y = − 6 and our goal is to isolate y on one side of the equation. This means we want to rewrite the equation in the form y = some expression involving x .
Isolating y To isolate y , we need to eliminate the term − 4 x from the left side of the equation. We can do this by adding 4 x to both sides of the equation. This maintains the equality and moves the − 4 x term to the right side.
Solving for y Adding 4 x to both sides of the equation − 4 x + y = − 6 , we get: − 4 x + y + 4 x = − 6 + 4 x Simplifying the left side, the − 4 x and + 4 x terms cancel each other out: y = − 6 + 4 x We can rewrite this as: y = 4 x − 6
Final Answer Therefore, the solution to the equation − 4 x + y = − 6 for y is y = 4 x − 6 .
Examples
In physics, this type of equation can represent the motion of an object. For example, if y represents the position of an object at time x , the equation y = 4 x − 6 tells us that the object's position increases by 4 units for every unit increase in time, starting from an initial position of -6. Understanding how to solve for y allows us to predict the object's position at any given time.
