To find the equation of this line in slope-intercept form, we need two main components:

1. Slope (m)
2. Y-intercept (b)

The slope-intercept form of a line is given by: $y = mx + b$

Step 1: Determine the Slope (m)

The slope $m$ is calculated as: $m = \frac{{\Delta y}}{{\Delta x}}$ From the graph, let's choose two points on the line for clarity:

• The point where $x = 0$ and $y = 4$ (the y-intercept)
• Another point, such as where $x = 4$ and $y = 0$

Now, using these points: $m = \frac{{0 - 4}}{{4 - 0}} = \frac{{-4}}{{4}} = -1$

Step 2: Determine the Y-intercept (b)

From the graph, we observe that the line crosses the y-axis at $y = 4$. Thus, the y-intercept $b$ is 4.

Final Equation

Substituting the values of $m$ and $b$ into the slope-intercept form: $y = -x + 4$

Answer

The equation of the line in slope-intercept form is: $y = -x + 4$

Would you like further clarification on any step?

Here are five related questions for deeper understanding:

1. How would you calculate the equation if you were given two points not on the y-axis?
2. What does a positive slope indicate about the direction of a line on a graph?
3. How would the equation change if the y-intercept were negative?
4. How can you verify if a given point lies on a specific line using its equation?
5. What would be the equation of a line parallel to this one but passing through a different y-intercept?

Tip: To check if your slope calculation is correct, try picking different pairs of points on the line and see if you obtain the same slope.