To write the equation of the line in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, we can use the two given points: $(0, 1)$ and $(4, 2)$.

Step 1: Calculate the slope

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(0, 1)$ and $(4, 2)$: $m = \frac{2 - 1}{4 - 0} = \frac{1}{4}$ So, the slope $m = \frac{1}{4}$.

Step 2: Identify the y-intercept

From the graph and the given point $(0, 1)$, the y-intercept $b$ is clearly $1$.

Step 3: Write the equation

Now that we have the slope $m = \frac{1}{4}$ and the y-intercept $b = 1$, the equation of the line in slope-intercept form is: $y = \frac{1}{4}x + 1$

Would you like more details or further clarification?

Here are five related questions to expand your understanding:

1. How would you find the equation if you were given different points?
2. What does the slope tell you about the direction of the line?
3. How would the equation change if the y-intercept were different?
4. Can the slope be negative? What would that look like on a graph?
5. How can you check if a point lies on a line given its equation?

Tip: Always check the y-intercept from the graph or the given points directly; it's the easiest way to get the full equation quickly!