Question

Rewrite the equation so that \(y\) is a function of \(x .\) $$4 x-3(y-2)=15+y$$

Short answer

The rewritten equation is \(y = -2x + 10.5 \)

Step-by-step solution

Distribute

Firstly, make sure to distribute the -3 to both terms inside the brackets on the left side of the equation. So the equation now becomes: \(4x - 3y + 6 = 15 + y\)

Arrange Terms

Next, collect the terms with \(y\) on one side of the equation and the constants on the other side. This can be done by subtracting \(y\) from both sides and subtracting 6 from both sides. The equation simplifies to: \(-3y + y = 4x - 15 - 6 \)

Simplify Equation

After simplifying the equation, we get: \(-2y = 4x - 21\)

Isolate y

Finally, divide every term by the coefficient of \(y\) which is -2. This will isolate \(y\) on one side of the equation, giving: \(y = -2x + 10.5\)