Final answer:
The expression a(3)=9 typically indicates a function a evaluated at x=3 gives a result of 9, which could represent a sequence or a functional relationship in different mathematical contexts. Additionally, the equation y = 9 + 3x depicts a linear function where 9 is the y-intercept and 3 is the slope.
Step-by-step explanation:
The best interpretation of a(3)=9 is that it represents the value of a function a when the argument x is 3. This can occur in different contexts, such as in sequences, where a could indicate the third term of the sequence is 9, or in functional notation where a(x) defines a function and when x is 3, the output is 9.
Exploring the rules and processes described, like xPx9 = x(p+q), it applies to expressions with exponential properties, where P and Q are exponents. For example, 3² and 3³ could be combined to result in 3²¹, which simplifies to 3⁵ or 3 to the power of 5, according to the rule of adding exponents when multiplying like bases.
For the equation y = 9 + 3x, this is a linear equation with a slope-intercept form, where 9 is the y-intercept (b term) and 3 is the slope (m term) of the line. Constructing a table or graphing this equation would involve choosing values for x, calculating y, and then plotting these points to visualize the line represented by the equation.