Final answer:
The equation 3(4y-12)=0 simplifies to y=3, which is a horizontal line crossing the y-axis at 3. Therefore, the graph of the given equation is best represented by option D) y=3 from the provided choices.
Step-by-step explanation:
The equation provided is 3(4y-12)=0. To graph the equation in slope-intercept form, we first need to solve for y. By dividing both sides of the equation by 3, we cancel out the left-side coefficient, leaving us with 4y-12=0. Adding 12 to both sides gives us 4y=12, and finally, dividing by 4 yields y=3.
This is a horizontal line and represents the slope-intercept form, which is usually given as y=mx+b, where m is the slope and b is the y-intercept. For our equation, the slope (m) is 0 since the line is horizontal, and the y-intercept (b) is 3. No x-term is needed because our line has no slope—it's horizontal.
Looking at the options given, we can see that the correct graph of the equation is described by D) y=3, which is a horizontal line crossing the y-axis at 3. It does not matter what the value of x is; y will always be 3. This corresponds with Figure 12.4 (b) from the reference, which illustrates that if b=0, the line is horizontal.