Understanding the Equation
The given equation is 3y + 6x + 2 = 0. To find the slope and y-intercept, we need to convert this equation into the slope-intercept form, which is expressed as y = mx + b, where m is the slope and b is the y-intercept.
Steps to Rearrange the Equation
- Start with the original equation:
3y + 6x + 2 = 0
- Isolate the term with y:
3y = -6x – 2
- Now, divide every term by 3 to solve for y:
y = -2x – rac{2}{3}
Identifying Slope and Y-Intercept
From the rearranged equation y = -2x – rac{2}{3}, we can easily identify the slope and y-intercept:
- Slope (m): -2
- Y-Intercept (b): -2/3 (which is approximately -0.67)
Conclusion
To conclude, for the equation 3y + 6x + 2 = 0, the slope is -2 and the y-intercept is - rac{2}{3}. This means that for every unit increase in x, the value of y decreases by 2 units. Additionally, the line crosses the y-axis at the point (0, -2/3).