The image shows a graph of a straight line, and the goal is to determine the equation of the line in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Identify the y-intercept $b$

The y-intercept is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at $(0, 2)$, so: $b = 2$

Step 2: Find the slope $m$

The slope $m$ is given by the formula: $m = \frac{\text{rise}}{\text{run}}$ From the graph, the line passes through two points: $(0, 2)$ and $(3, 5)$.

• Rise = $5 - 2 = 3$
• Run = $3 - 0 = 3$

Thus, the slope is: $m = \frac{3}{3} = 1$

Final Equation

Substituting $m = 1$ and $b = 2$ into the equation $y = mx + b$, we get: $y = x + 2$

Conclusion

The equation of the line is: $y = x + 2$

Would you like more details on this process or additional practice problems? Here are five related questions to explore further:

1. How do you find the equation of a line given two points?
2. What is the equation of a line parallel to this one but passing through $(0, -3)$?
3. How do you calculate the slope of a vertical line?
4. Can you identify a line with a negative slope from a graph?
5. What happens to the equation if you change the slope to $2$ and keep the y-intercept the same?

Tip: The slope tells you how steep a line is, and the sign (positive or negative) determines its direction.