The task is to determine the equation of the line displayed in the graph in terms of $x$. Let’s analyze the graph step-by-step:

Step 1: Determine the slope ($m$)

The slope formula is: $m = \frac{\text{change in } y}{\text{change in } x}$

Using the points visible on the graph:

• The line passes through $(-3, 4)$ and $(3, -2)$.

Calculate the slope: $m = \frac{-2 - 4}{3 - (-3)} = \frac{-6}{6} = -1$

Step 2: Determine the y-intercept ($b$)

The y-intercept is where the line crosses the $y$-axis ($x = 0$). From the graph, it crosses the $y$-axis at $b = 1$.

Step 3: Write the equation

The equation of the line in slope-intercept form is: $y = mx + b$ Substitute $m = -1$ and $b = 1$: $y = -x + 1$

Final Answer:

$y = -x + 1$

Let me know if you want further clarifications or detailed explanations!

Expanding the concept:

1. How can you verify the slope with other points on the line?
2. What is the importance of identifying the y-intercept?
3. Could this line be written in another form, such as standard form?
4. How does the slope change for parallel and perpendicular lines?
5. What happens to the equation if the graph is shifted up or down?

Tip: Always double-check your slope calculations by selecting two clear points from the graph!