To analyze the graph and determine which equation best describes the line:

Step-by-step breakdown:

1. Identify the slope: The line rises by 2 units for every 1 unit it moves to the right, indicating a slope of $\frac{2}{1} = 2$.

2. Identify the y-intercept: The line crosses the y-axis at $y = 4$.

General form of the equation:

The equation of a line in slope-intercept form is: $y = mx + b$ Where:

• $m$ is the slope.
• $b$ is the y-intercept.

From the graph:

• Slope $m = 2$.
• Y-intercept $b = 4$.

Thus, the equation of the line is: $y = 2x + 4$

Conclusion:

The correct equation is $y = 2x + 4$, which matches the first option in the list.

Would you like further details or have any questions?

Here are some related questions:

1. What is the significance of the slope in the graph?
2. How do you calculate the slope of a line from a graph?
3. Can the slope be negative, and how would the graph look in that case?
4. How does changing the y-intercept affect the graph?
5. How can you identify a linear equation if given a different form (e.g., standard form)?

Tip: To find the slope of a line on a graph, choose two points and calculate the change in $y$ divided by the change in $x$ (rise over run).