To find the equation of a line passing through two points, we’ll use the formula for the slope $m$ and the point-slope form of a line. Here’s the step-by-step solution:

Step 1: Find the Slope

The points given are $(-2, 4)$ and $(3, -6)$.

The slope $m$ is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6 - 4}{3 - (-2)} = \frac{-10}{5} = -2$

Step 2: Use the Point-Slope Form

Now, we use the point-slope form $y - y_1 = m(x - x_1)$. Using the slope $m = -2$ and one of the points, say $(-2, 4)$:

$y - 4 = -2(x + 2)$

Step 3: Simplify to Slope-Intercept Form

Expand and simplify to get the equation in $y = mx + b$ form:

$y - 4 = -2x - 4$ $y = -2x$

Conclusion

The correct equation