Understanding the Equation Y = 2X + 4
The equation Y = 2X + 4 represents a linear function in the form of y = mx + b, where 2 is the slope of the line and 4 is the y-intercept. The slope of 2 indicates that for every unit increase in x, y increases by 2 units. The y-intercept of 4 means that the line intersects the y-axis at the point (0, 4).
How to Plot Points to Create the Graph
To plot the graph of the function Y = 2X + 4, we can start by finding a few points that lie on the line. We can choose different values of x and substitute them into the equation to find the corresponding y-values. Here are some points:
- When x = 0, y = 4
- When x = 1, y = 2(1) + 4 = 6
- When x = -1, y = 2(-1) + 4 = 2
Plotting the Graph
Now that we have a few points, we can plot them on a graph and connect them with a straight line to represent the function Y = 2X + 4.
Which Graph Represents the Function Y = 2X + 4?
There are three possible types of graphs that could represent the function Y = 2X + 4:
- A straight line with a positive slope: Since the coefficient of x is positive (2), the graph should have a positive slope. The line should be going upwards as x increases.
- A line passing through the point (0,4): The y-intercept of the function is 4, which means the line should pass through the point (0,4) on the y-axis.
- A linear function: The function Y = 2X + 4 is a linear function, which means the graph should be a straight line.
Comparing Graphs
Let’s compare the characteristics of the function Y = 2X + 4 with different types of graphs to determine which one represents the function accurately:
- Graph A: A straight line with a positive slope but not passing through (0,4).
- Graph B: A straight line with a positive slope passing through (0,4).
- Graph C: A parabolic curve.
Analysis of Graphs
Now, let’s analyze each graph in detail to determine which one accurately represents the function Y = 2X + 4:
Graph A
Graph A is a straight line with a positive slope but does not pass through the point (0,4). Since the y-intercept of the function is 4, this graph does not accurately represent the function Y = 2X + 4.
Graph B
Graph B is a straight line with a positive slope passing through the point (0,4). This graph accurately represents the function Y = 2X + 4 as it exhibits both the correct slope and the correct y-intercept.
Graph C
Graph C is a parabolic curve, which is not a linear function. Since the function Y = 2X + 4 is a linear equation, this graph does not accurately represent the function.
Conclusion
After analyzing the characteristics of each graph, it is evident that Graph B, a straight line with a positive slope passing through the point (0,4), accurately represents the function Y = 2X + 4. It exhibits both the correct slope and y-intercept of the function.
