Question

put the following equation of a line into slope-intercept form, simplifying all fractions.
4x + 6y = 36

Explanation:

Step1: Isolate the y-term

Subtract \(4x\) from both sides of the equation \(4x + 6y = 36\) to get \(6y=-4x + 36\).

Step2: Solve for y

Divide every term by 6. So, \(y=\frac{-4x}{6}+\frac{36}{6}\). Simplify the fractions: \(\frac{-4}{6}\) simplifies to \(-\frac{2}{3}\) and \(\frac{36}{6}\) simplifies to 6. Thus, \(y = -\frac{2}{3}x+6\).

Answer:

\(y = -\frac{2}{3}x + 6\)