To find the equation of the line shown in the graph, let's follow these steps:

1. Determine the slope ($m$): The slope is the change in $y$ divided by the change in $x$ ($m = \frac{\Delta y}{\Delta x}$).

   From the graph:

   • One point is $(-4, 0)$.
   • Another point is $(0, 2)$.

   Calculate the slope: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{0 - (-4)} = \frac{2}{4} = \frac{1}{2}.$

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

3. Write the equation: Using the slope-intercept form of a line, $y = mx + b$, substitute $m = \frac{1}{2}$ and $b = 2$: $y = \frac{1}{2}x + 2.$

Final Answer:

The equation of the line is: $y = \frac{1}{2}x + 2$

Let me know if you need further clarifications or calculations.

Related Questions:

1. What is the significance of the slope in a line equation?
2. How can you identify the x-intercept from the given equation?
3. What is the general form of a linear equation, and how does it relate to this example?
4. How would the equation change if the line had a different slope?
5. Can you verify the equation by substituting additional points on the graph?

Tip:

Always double-check the slope by ensuring the same ratio applies for any two distinct points on the line.