Final answer:
To convert 2x+3y=12 into slope-intercept form, isolate y on one side of the equation to get y = (-2/3)x + 4, where the slope is -2/3 and the y-intercept is 4.
Step-by-step explanation:
To convert the standard form equation 2x+3y=12 into the slope-intercept form, you need to solve for y in terms of x, which is generally represented as y = mx + b, where 'm' is the slope and 'b' is the y-intercept. Here's the step-by-step process:
- 2x + 3y = 12 (Original equation)
- Subtract 2x from both sides: 3y = -2x + 12
- Divide all terms by 3: y = (-2/3)x + 4
In this form, y = (-2/3)x + 4, the slope (m) is -2/3, indicating a rise of 2 units down (since it's negative) for every 3 units we move to the right on the horizontal axis. The y-intercept (b) is 4, showing where the line crosses the y-axis.