Which of the following graphs represents the function y = x + 3?
Graph B
Graph A
Graph D
Graph C
Graph D
To determine which graph represents the function y = x + 3, we need to analyze the equation and compare it to the graphs.
The equation y = x + 3 represents a linear function with a slope of 1 (the coefficient of x) and a y-intercept of 3 (the constant term).
Let's examine each graph:
Graph A:
This graph does not have a y-intercept at 3. It has a y-intercept around -1, so it does not represent the function y = x + 3.
Graph B:
This graph does have a y-intercept at 3, and it appears to have the correct slope of 1. So, Graph B represents the function y = x + 3.
Graph C:
This graph also does not have a y-intercept at 3. It has a y-intercept around -3, so it does not represent the function y = x + 3.
Graph D:
This graph has a y-intercept of 0 and a horizontal line. It does not have a slope of 1, so it is not a representation of the function y = x + 3.
Based on this analysis, the correct answer is Graph B.