Question

put the following equation of a line into slope-intercept form, simplifying all fractions.
6y - 3x = -12

Explanation:

Step1: Isolate the y-term

We start with the equation \(6y - 3x = -12\). First, we need to isolate the term with \(y\) on one side. So we add \(3x\) to both sides of the equation.

$$6y - 3x + 3x = 3x - 12$$

Simplifying the left side (the \(-3x\) and \(+3x\) cancel out) and the right side remains as is, we get:

$$6y = 3x - 12$$

Step2: Solve for y

Now, we want to solve for \(y\) by dividing every term in the equation by \(6\) (the coefficient of \(y\)).

$$y=\frac{3x}{6}-\frac{12}{6}$$

Simplify each fraction. \(\frac{3x}{6}\) simplifies to \(\frac{1}{2}x\) and \(\frac{12}{6}\) simplifies to \(2\). So the equation becomes:

$$y = \frac{1}{2}x - 2$$

Answer:

\(y=\frac{1}{2}x - 2\)