Final answer:
The equation 9x+7y=3 does define y as a function of x because it can be rearranged to express y solely in terms of x, proving that for each x value, there is one corresponding y value.
Step-by-step explanation:
The question asks to state whether the equation 9x+7y=3 defines y as a function of x. To determine if y is a function of x, we need to be able to express y in terms of x such that for every value of x, there is only one corresponding value of y. Let's manipulate the given equation:
- 9x + 7y = 3
- 7y = 3 - 9x
- y = (3 - 9x)/7
Now, y is expressed as a function of x, which, when graphed, will create a straight line. This means that for each value of x, there is exactly one value of y, satisfying the definition of a function. Hence, the equation 9x + 7y = 3 does define y as a function of x.
The linear equation presented is similar to other equations like y = 9 + 3x, where b and m are constants and y is a function of x. When these linear equations are graphed, each x value corresponds to one y value, further illustrating the concept of a function.