To find the slope of the line given by the equation 4x + 6y = 12, we first need to rearrange it into the slope-intercept form, which is y = mx + b, where m represents the slope and b is the y-intercept.
Here are the steps to rearrange the equation:
- Start with the original equation: 4x + 6y = 12.
- Subtract 4x from both sides: 6y = -4x + 12.
- Now, divide every term by 6 to solve for y: y = - rac{4}{6}x + 2.
- Simplifying -4/6 gives us -2/3, thus the equation becomes: y = - rac{2}{3}x + 2.
Now we can easily see that the slope (m) of the line is - rac{2}{3}.
In conclusion, the slope of the line 4x + 6y = 12 is - rac{2}{3}.