To find the slope of the line given by the equation 4x + 6y = 12, we need to rearrange the equation into the slope-intercept form, which is y = mx + b. In this form, m represents the slope of the line.
Start by isolating y:
- Subtract 4x from both sides of the equation:
- 6y = 12 – 4x
Next, divide every term by 6 to solve for y:
- y = 2 – rac{4}{6}x
- y = 2 – rac{2}{3}x
Now, rewrite the equation in the slope-intercept form:
y = - rac{2}{3}x + 2
From this form, we see that the slope (m) of the line is - rac{2}{3}.
In summary, the slope of the line represented by the equation 4x + 6y = 12 is - rac{2}{3}.