Final answer:
The correct graph that represents the equation 3x + 2y = 24 is graph (a).
Step-by-step explanation:
The correct graph that represents the equation 3x + 2y = 24 is graph (a). To determine the equation’s graph, we can convert the given equation into slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept. Rearranging the equation, we have 2y = -3x + 24, and dividing both sides by 2 gives us y = -3/2x + 12. This form shows that the slope is -3/2 and the y-intercept is 12. In graph (a), the line slopes downward to the right, consistent with a negative slope, and passes through the y-axis at 12, as expected.