Final answer:
The value of y is approximately -6937.5 when x is -9 1/4 in the direct variation equation y = kx, with the constant of variation k = 750.
Step-by-step explanation:
To find the value of y when x is -9 1/4, we need to use the concept of direct variation. In a direct variation, the ratio of y to x remains constant. We can write the direct variation equation as y = kx, where k is the constant of variation.
First, let's find the value of k using the given values of y = 375 and x = 1/2:
k = y/x = 375 / (1/2) = 375 * 2 = 750.
Now, substitute the value of x = -9 1/4 into the equation:
y = 750 * (-9 1/4) = -6750 + (-750/4) = -6750 - 187.5 = -6937.5.
Therefore, when x is -9 1/4, the value of y is approximately -6937.5.