Put the following equation of a line into slope-intercept form, simplifying all fractions.
6, x, minus, 5, y, equals, minus, 5
6x−5y=
−5

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.

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

Learn how to convert the linear equation 6x - 5y = -5 into slope-intercept form. This problem covers key algebraic concepts, including solving for y, simplifying fractions, and identifying slope and y-intercept. Suitable for students in Grades 8-10.

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