Let's analyze the graph to determine the equation of the line.

The line appears to be straight, meaning the equation will be of the form $y = mx + b$, where:

• $m$ is the slope.
• $b$ is the y-intercept (the value where the line crosses the y-axis).

Step 1: Identify the y-intercept

From the graph, we can see that the line crosses the y-axis at $(0, 1)$. Therefore, $b = 1$.

Step 2: Determine the slope

To calculate the slope $m$, we use two points on the line. The graph shows the line passing through the points $(0, 1)$ and $(1, 3)$.

The formula for slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the points $(0, 1)$ and $(1, 3)$:

$m = \frac{3 - 1}{1 - 0} = \frac{2}{1} = 2$

Thus, the slope is $m = 2$.

Step 3: Write the equation

Now that we have $m = 2$ and $b = 1$, the equation of the line is:

$y = 2x + 1$

Conclusion:

The correct answer is $y = 2x + 1$, which matches the first option.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. How do you determine the slope of a line from a graph?
2. What is the significance of the y-intercept in the equation of a line?
3. How would the equation change if the line had a negative slope?
4. How can you verify if a point lies on a given line?
5. What happens to the equation if the line shifts vertically?

Tip: Always check at least two points on the graph to ensure the accuracy of the slope calculation.