Answer:
Step-by-step explanation:The given function is y = 3x. To determine whether this function is a linear function, need to check if it satisfies the definition of a linear function, which states that the function must have a constant rate of change.
In a linear function, the rate of change, or slope, remains constant throughout the entire graph. To check if the function y = 3x has a constant rate of change, we can calculate the difference in y-values (Δy) and the difference in x-values (Δx) between any two points on the graph.
choose two arbitrary points on the graph to calculate the rate of change:
Point A: (x₁, y₁) = (0, 0)
Point B: (x₂, y₂) = (2, 6)
Now, calculate the rate of change (slope) using the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
slope = (6 - 0) / (2 - 0) = 6 / 2 = 3
The calculated slope is 3, which is a constant value. Therefore, the function y = 3x satisfies the definition of a linear function and has a constant rate of change.
In conclusion, the given function y = 3x is a linear function.