To find the equation of the line from the graph, we need to determine two key components: the slope and the y-intercept. Here's how we can proceed:

1. Identifying two points on the line

From the graph, we can see two points that the line passes through:

• Point 1: $(-4, 2)$
• Point 2: $(4, -2)$

2. Finding the slope (m)

The slope formula is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the coordinates of the points: $m = \frac{-2 - 2}{4 - (-4)} = \frac{-4}{8} = -\frac{1}{2}$

3. Using the slope-intercept form

The general equation of a line is: $y = mx + b$ We already know that $m = -\frac{1}{2}$, so the equation is:

$y = -\frac{1}{2}x + b$

4. Finding the y-intercept (b)

To find $b$, we can substitute the coordinates of one of the points (let's use $(-4, 2)$) into the equation:

$2 = -\frac{1}{2}(-4) + b$ $2 = 2 + b \implies b = 0$

Thus, the equation of the line is: $y = -\frac{1}{2}x$

This is the equation of the line based on the graph.

Do you want more details or have any questions?

Further related questions:

1. How do we find the slope if the points aren't directly visible on the graph?
2. What does the slope represent in terms of steepness or direction?
3. How can we confirm that a point lies on the line?
4. How would the equation change if the line were parallel or perpendicular to the current one?
5. What is the general form of the line equation, and how does it relate to the slope-intercept form?

Tip: Always choose clearly identifiable points on the graph to ensure the most accurate slope calculation.