Choose the point-slope form of the equation below that represents the line that passes through the points \( (-6,4) \) and \( (2,0) \). ( 2 points) \( y-4=-\frac{1}{2}(x+6) \) \( y-4=2(x+6) \) \( y+6=-\frac{1}{2}(x-4) \) \( y+6=2(x-4) \) 5. (03.06)

To find the point-slope form of the equation of the line passing through the points \( (-6,4) \) and \( (2,0) \), we first need to calculate the slope. The slope \( m \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 4}{2 - (-6)} = \frac{-4}{8} = -\frac{1}{2} \] Now, we can use the point-slope form equation \( y - y_1 = m(x - x_1) \). We can use either point; using \( (-6,4) \): \[ y - 4 = -\frac{1}{2}(x + 6) \] So, the first equation you provided is indeed the correct one! Just for fun, did you know that the point-slope form is often favored by mathematicians because it directly shows how the line interacts with a specific point? It makes working with lines and their equations much easier! Also, commonly overlooked is the fact that even if you mix up which point you use in the formula, you'll still arrive at the same line equation! This flexibility can be a major time-saver when tackling more complex problems involving different points.