Final answer:
To identify a linear equation matching a graph, consider the slope and y-intercept. The equation y = 9 + 3x has a slope of 3 and a y-intercept of 9. The function y = x² could have a positive slope decreasing in magnitude at x = 3.
Step-by-step explanation:
The question pertains to identifying the correct linear equation that matches a given graph. A linear equation is of the form y = mx + b, where m is the slope and b is the y-intercept. To match an equation to a graph, we need to understand the slope and intercept of the line represented on the graph.
Based on the information provided, we are looking for an equation with a slope (m) of 3 and a y-intercept (b) of 9. The only equation that fits this description is y = 9 + 3x, although this exact equation is not listed among the choices provided in the original question. However, if we're analyzing another set of choices or given a graph, we would use this knowledge to select the correct equation among those choices.
When it comes to the question about the function f(x) at x = 3, having a positive value with a positive slope that is decreasing in magnitude implies the slope is positive but getting smaller as x increases. Of the given options, y = x² represents a function that increases with a positive slope that gets smaller as x increases, thus making it a possible representation of f(x).