Question

put the following equation of a line into slope - intercept form, simplifying all fractions.
$5x + 6y = 6$

Explanation:

Step1: Isolate the y - term

We start with the equation \(5x + 6y=6\). To isolate the \(y\) - term, we subtract \(5x\) from both sides of the equation.
\(6y=- 5x + 6\)

Step2: Solve for y

We divide every term in the equation \(6y=-5x + 6\) by \(6\) to solve for \(y\).
\(y=\frac{-5x + 6}{6}\)
We can simplify this fraction by splitting the numerator:
\(y =-\frac{5}{6}x+\frac{6}{6}\)
Since \(\frac{6}{6} = 1\), we get:
\(y=-\frac{5}{6}x + 1\)

Answer:

\(y =-\frac{5}{6}x+1\)