Final answer:
To convert 2x+3y=-9 into slope-intercept form, subtract 2x from both sides, and then divide each term by 3 to isolate y. The result is y = (-2/3)x - 3, with a slope of -2/3 and a y-intercept of -3.
Step-by-step explanation:
To convert the standard form equation 2x+3y=-9 into slope-intercept form, you will need to solve the equation for y. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Here are the steps:
- Start with the given equation: 2x + 3y = -9.
- Subtract 2x from both sides to get: 3y = -2x - 9.
- Divide every term by 3 to solve for y: y = (-2/3)x - 3.
In the equation y = (-2/3)x - 3, the slope (m) is -2/3 and the y-intercept (b) is -3. This means that the line crosses the y-axis at (0, -3) and for every unit that x increases, y decreases by 2/3 of a unit.