How do you find the slope of the line represented by the equation 2x + 3y + 6 = 0?

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To find the slope of the line represented by the equation 2x + 3y + 6 = 0, you need to first rewrite the equation in the slope-intercept form, which is y = mx + b. In this form, m represents the slope of the line, and b represents the y-intercept.

Here are the steps to rewrite the equation:

  1. Start with the original equation:
    2. 2x + 3y + 6 = 0
  2. Isolate the term with y:
    3. 3y = -2x - 6
  3. Divide each term by 3 to solve for y:
    4. y = -rac{2}{3}x - 2

Now, the equation is in the slope-intercept form:

y = -rac{2}{3}x - 2

From this equation, you can see that the slope (m) is - rac{2}{3}. Therefore, the slope of the line represented by the given equation is:

Slope: -2/3

This means that for every 3 units you move to the right along the x-axis, you move down 2 units along the y-axis, indicating a negative slope that results in a line that slants downwards from left to right.

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