To find the equation of the line in slope-intercept form, $y = mx + b$, we need to identify the slope ($m$) and the y-intercept ($b$).

Step 1: Identify the Slope ($m$)

The slope ($m$) is the rise over the run between two points on the line. From the graph:

1. We have one point at $(0, 2)$.
2. Another point is at $(4, 6)$.

The slope is calculated as: $m = \frac{{\text{{rise}}}}{{\text{{run}}}} = \frac{{6 - 2}}{{4 - 0}} = \frac{4}{4} = 1$

So, $m = 1$.

Step 2: 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 $(0, 2)$. Therefore, $b = 2$.

Step 3: Write the Equation

Now that we have $m = 1$ and $b = 2$, the equation of the line is: $y = 1x + 2 \quad \text{or simply} \quad y = x + 2$

So, the equation of the line is $\boxed{y = x + 2}$.

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Related Questions

1. How do you find the slope of a line if only two points are given?
2. What happens to the equation if the slope is negative?
3. How would you convert a point-slope form equation into slope-intercept form?
4. What is the significance of the y-intercept in a real-world scenario?
5. How can you determine if two lines are parallel or perpendicular using their slopes?

Tip

Remember, the slope is the change in $y$ over the change in $x$. If the slope is positive, the line rises; if it’s negative, the line falls.