To find the equation of the line shown in the graph, we'll first identify two key pieces of information: the slope ($m$) and the y-intercept ($b$).

Step 1: Determine the Slope ($m$)

The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

From the graph:

• One point on the line is $(-5, 5)$.
• Another point is $(5, -5)$.

Using these points, the slope $m$ is calculated as follows: $m = \frac{\text{rise}}{\text{run}} = \frac{-5 - 5}{5 - (-5)} = \frac{-10}{10} = -1$

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

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

Step 3: Write the Equation

Now that we have the slope $m = -1$ and the y-intercept $b = 0$, the equation of the line in slope-intercept form $y = mx + b$ is: $y = -x$

So, the equation of the line is $y = -x$.

Would you like any further details or explanations on this? Here are some additional related questions you might consider:

1. How would the equation change if the slope were positive?
2. What is the significance of the y-intercept in a linear equation?
3. How can you use the equation to find the x-intercept?
4. What would happen if the slope were zero?
5. How does the slope affect the angle of the line relative to the x-axis?

Tip: Remember that the slope of a line indicates its steepness and direction. A negative slope means the line goes down as you move from left to right.