The given graph shows a straight line passing through the coordinate plane. Let's analyze its equation step by step.

1. Identify Two Points

From the graph, we can identify two points on the line:

• $(-6, 6)$
• $(6, -6)$

2. Calculate the Slope ($m$)

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the given points: $m = \frac{-6 - 6}{6 - (-6)} = \frac{-12}{12} = -1$

3. Find the Equation in Slope-Intercept Form

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

To find $b$, substitute one of the given points, say $(-6, 6)$:

$6 = -(-6) + b$ $6 = 6 + b$ $b = 0$

4. Final Equation

$y = -x$

This is the equation of the given line.

Would you like a step-by-step verification or explanation on any specific part?

Here are five related questions for further exploration:

1. What happens to the line if the slope changes to a positive value?
2. How can you determine the equation of a line given a point and a slope?
3. What is the perpendicular slope to this line?
4. How do you find the x- and y-intercepts of any linear equation?
5. Can you express this equation in standard form?

Tip: The negative slope indicates the line is decreasing from left to right.