To find the slope of the line represented by the equation 6x + 8y = 12, we first need to rearrange this equation into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
We start with the original equation:
6x + 8y = 12
Next, we isolate y by subtracting 6x from both sides:
8y = -6x + 12
Now, we divide every term by 8:
y = - rac{6}{8}x + rac{12}{8}
We simplify the fractions:
y = - rac{3}{4}x + rac{3}{2}
From the equation y = - rac{3}{4}x + rac{3}{2}, we can see that the slope m is - rac{3}{4}.
Thus, the slope of the line is -0.75.