To put the equation $6x - 5y = -5$ into slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, follow these steps:

Step 1: Solve for $y$

Start by isolating $y$ on one side of the equation: $6x - 5y = -5$

Subtract $6x$ from both sides: $-5y = -6x - 5$

Step 2: Divide by $-5$

Now, divide the entire equation by $-5$ to solve for $y$: $y = \frac{-6x - 5}{-5}$

Step 3: Simplify the fractions

Simplify each term: $y = \frac{-6x}{-5} + \frac{-5}{-5}$

This simplifies to: $y = \frac{6}{5}x + 1$

Final Answer:

The equation in slope-intercept form is: $y = \frac{6}{5}x + 1$

Would you like any additional details or have any questions?

Here are 5 related questions:

1. How do you find the slope from two points on a line?
2. What is the significance of the y-intercept in a line equation?
3. How do you convert a line equation from standard form to slope-intercept form?
4. How can you graph a line using the slope-intercept form?
5. What are the steps to determine if two lines are parallel or perpendicular?

Tip: The slope-intercept form $y = mx + b$ is very useful for quickly identifying the slope $m$ and the y-intercept $b$ of a line.