To find the slope of the line given by the equation 2x + 3y – 6 = 0, we need to rearrange the equation into slope-intercept form, which is y = mx + b, where m represents the slope.
Starting with the original equation:
2x + 3y - 6 = 0
We can isolate y:
3y = -2x + 6
Now, divide every term by 3 to solve for y:
y = - rac{2}{3}x + 2
From this equation, we can see that the slope (m) is -2/3. This means that for every 3 units you move to the right along the x-axis, the line goes down 2 units.