Final answer:
The equation 3x + 2y = 6 represents a linear function when written in slope-intercept form, as it takes the form y = mx + b. Therefore, the correct description for the function is linear, and not arithmetic, geometric, or exponential.
Step-by-step explanation:
The student's question involves the equation 3x + 2y = 6 and determining the characteristics of the function it represents. To describe the function, we must first rewrite the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
By solving for y, we get 2y = -3x + 6, and then y = -1.5x + 3. This is in the form of a linear equation, which is an equation of the first degree, meaning its graph is a straight line. We can therefore describe the function as:
- Linear: Because it can be expressed as y = mx + b with m and b being constants.
The equation is not an arithmetic sequence because it does not describe a sequence where each term is obtained by adding a constant, nor is it a geometric sequence, which involves a common ratio between terms. Additionally, it is not an exponential function, which would involve the variable in the exponent.