What is the slope-intercept form of the linear equation 2x + 3y = 6?

Question

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Answer 1

To convert the linear equation \(2x + 3y = 6\) into slope-intercept form, we need to solve for \(y\).

1. Start with the original equation: \[ 2x + 3y = 6 \]

2. Isolate \(3y\) by subtracting \(2x\) from both sides: \[ 3y = -2x + 6 \]

3. Now, divide everything by \(3\) to solve for \(y\): \[ y = -\frac{2}{3}x + 2 \]

Now that we have \(y\) in terms of \(x\), the slope-intercept form of the equation is: \[ y = mx + b \] where \(m\) is the slope and \(b\) is the y-intercept.

From the equation \(y = -\frac{2}{3}x + 2\):

• The slope \(m = -\frac{2}{3}\)
• The y-intercept \(b = 2\)

If you need to fill in specific boxes based on your question format, they may need to be filled out as follows:

• Slope (m): \(-\frac{2}{3}\)
• y-intercept (b): \(2\)

Please confirm if you need further assistance!

Answer 2

put it all in order

Answer 3

Sure! The slope-intercept form of the linear equation \(2x + 3y = 6\) is:

\[ y = -\frac{2}{3}x + 2 \]

In order:

1. Slope (m): \(-\frac{2}{3}\)
2. Y-intercept (b): \(2\)

If you're putting these in specific boxes, they would be:

• Slope (m): \(-\frac{2}{3}\)
• Y-intercept (b): \(2\)

Let me know if you need further assistance!