What is the slope of the line represented by the equation 3x + 4y = 12?

To find the slope of the line represented by the equation 3x + 4y = 12, we first need to rewrite the equation in the slope-intercept form, which is y = mx + b, where m represents the slope and b is the y-intercept.

Starting with the original equation:

3x + 4y = 12

We can isolate y by first subtracting 3x from both sides:

4y = -3x + 12

Next, we divide every term by 4 to solve for y:

y = (-3/4)x + 3

Now that the equation is in slope-intercept form, we can easily identify the slope. The coefficient of x in this equation, which is -3/4, indicates the slope of the line.

Therefore, the correct answer is that the slope of the line is -3/4. This negative slope indicates that as x increases, y decreases, which is characteristic of a line that moves downward from left to right on a graph.