Final answer:
To convert 3x + 2y = -6 to slope-intercept form y = mx + b, subtract 3x from both sides to get 2y = -3x - 6, then divide everything by 2 to solve for y, resulting in y = -1.5x - 3. This displays the slope (m) as -1.5 and the y-intercept (b) as -3.
Step-by-step explanation:
Converting to Slope-Intercept Form
To convert the equation 3x + 2y = -6 into the slope-intercept form, we need to solve for y to get an equation that looks like y = mx + b, where m represents the slope and b is the y-intercept. Follow these steps to transform the equation:
- Subtract 3x from both sides to isolate the y-term on one side: 2y = -3x - 6.
- Divide all terms by 2 to solve for y: y = -1.5x - 3.
This new equation, y = -1.5x - 3, is in slope-intercept form. The slope (m) is -1.5, and the y-intercept (b) is -3. Now you can easily identify the slope and y-intercept of the line, and you can graph it accordingly.
The concepts of slope and y-intercept, or additional examples, but for a complete answer, what's given here is ample to solve the mathematical problem completely. Remember, the slope is the rate of change of y with respect to x, and the y-intercept is the point where the line crosses the y-axis.