Write each equation in slope-intercept form.
6x+7y=77

To write the equation \(6x + 7y = 77\) in slope-intercept form, which is \(y = mx + b\) where \(m\) is the slope and \(b\) is the y-intercept, follow these steps:

1. Start with the equation:
   \[
   6x + 7y = 77
   \]

2. Subtract \(6x\) from both sides:
   \[
   7y = -6x + 77
   \]

3. Divide both sides by 7 to solve for \(y\):
   \[
   y = \frac{-6}{7}x + \frac{77}{7}
   \]

4. Simplify the constant term:
   \[
   y = \frac{-6}{7}x + 11
   \]

Thus, the equation in slope-intercept form is:
\[
y = \frac{-6}{7}x + 11
\]

Would you like further details on how the slope or intercept is determined, or do you have any other questions?

### Related questions:
1. What is the slope and y-intercept of the equation you just solved?
2. How can you convert slope-intercept form back to standard form?
3. What does the slope represent in this particular equation?
4. How would you graph the equation \(y = \frac{-6}{7}x + 11\)?
5. How can you find the x-intercept of the equation in slope-intercept form?

### Tip: 
In slope-intercept form, the coefficient of \(x\) (the slope) tells you how steep the line is, while the constant term (the y-intercept) shows where the line crosses the y-axis.

Write each equation in slope-intercept form. 6x + 7y = 77

Learn how to convert the equation 6x + 7y = 77 into slope-intercept form (y = mx + b) with a detailed, step-by-step solution. This problem explains how to find the slope and y-intercept, suitable for students in Grades 7-9.

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