The new image shows a coordinate plane with another line, but this time, it appears to have a negative slope. Let's analyze this line to determine its equation.

Step-by-Step Analysis

1. Identify the Points: The line passes through approximately the points $(-7, 10)$ and $(7, -10)$.

2. Calculate the Slope (m) of the Line: The slope $m$ can be found using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ where $(x_1, y_1) = (-7, 10)$ and $(x_2, y_2) = (7, -10)$.

3. Compute the Slope: $m = \frac{-10 - 10}{7 - (-7)} = \frac{-20}{14} = -\frac{10}{7}.$

4. Determine the Equation of the Line: Using the point-slope form of a linear equation: $y - y_1 = m(x - x_1),$ substitute $m = -\frac{10}{7}$ and one of the points, say $(-7, 10)$: $y - 10 = -\frac{10}{7} (x + 7).$

   Simplify this equation: $y = -\frac{10}{7}x.$

Equation of the Line

Thus, the equation of the line is:

$f(x) = -\frac{10}{7}x.$

Conclusion

The line passes through the origin $(0, 0)$ with a slope of $-\frac{10}{7}$, indicating that it is decreasing as $x$ increases.

Would you like more details or have any questions? Here are some related topics:

1. How to find the x-intercept of a line.
2. Difference between positive and negative slopes.
3. How to derive the equation from different points on a line.
4. Understanding perpendicular and parallel lines.
5. Calculating the midpoint between two points on a line.

Tip: A negative slope means that as $x$ increases, $y$ decreases, which is why the line goes down from left to right.