Question

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

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We need to solve the given equation \(6x-5y=-5\) for \(y\).

Step2: Isolate the \(y\) - term

Subtract \(6x\) from both sides of the equation \(6x - 5y=-5\).
We get \(-5y=-6x - 5\). The reason for this step is to get the term with \(y\) alone on one side of the equation. When we subtract \(6x\) from both sides, we are using the subtraction property of equality, which states that if \(a = b\), then \(a - c=b - c\) for any real number \(c\).

Step3: Solve for \(y\)

Divide every term in the equation \(-5y=-6x - 5\) by \(-5\).
For the first term: \(\frac{-5y}{-5}=\frac{-6x}{-5}+\frac{-5}{-5}\)
Simplifying each term, we have \(y=\frac{6}{5}x + 1\). When we divide by \(-5\), we are using the division property of equality, which states that if \(a = b\), then \(\frac{a}{c}=\frac{b}{c}\) for \(c
eq0\).

Answer:

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