Final answer:
Category A) includes rational numbers x and y, while category B) includes the irrational number z. Linear equations have the form y = mx + b, and examples include y = -3x, y = 0.2 +0.74x, and y=-9.4 - 2x, all of which are linear.
Step-by-step explanation:
The question involves categorizing numbers into rational and irrational. We are asked to match x and y as non-zero rational numbers and z as an irrational number. In mathematics, a rational number is any number that can be expressed as the quotient or fraction ⁄ of two integers, a numerator and a non-zero denominator. An irrational number, on the other hand, cannot be expressed as a simple fraction and its decimal form does not terminate or repeat.
- A) x, y would both be categorized as rational numbers.
- B) z would be categorized as an irrational number.
When considering linear equations, we have examples such as y = -3x, y = 0.2 +0.74x, and y=-9.4 - 2x, all of which can be represented by the general form y = mx + b, where m is the slope and b is the y-intercept. Given that x is the independent variable and y is the dependent variable, we choose a value to substitute for x and solve for y.