Question

a circle representing a pool is graphed with a center at the origin. grant enters the pool at point a and swims over to a friend who is located at point b. which equation represents grant’s path?
( y = 2 - 4x )
( y = 4 - \frac{x}{2} )
( y = 6 - \frac{x}{4} )
( y = 8 - 2x )

Explanation:

Step1: Identify coordinates of points

From the graph, point A is at \((8, 0)\) and point B is at \((-4, 6)\).

Step2: Calculate the slope

The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 8\), \(y_1 = 0\), \(x_2=-4\), \(y_2 = 6\):
\(m=\frac{6 - 0}{-4 - 8}=\frac{6}{-12}=-\frac{1}{2}\)

Step3: Use point - slope form

Using point A \((8, 0)\) and slope \(m =-\frac{1}{2}\) in the point - slope form \(y - y_1=m(x - x_1)\):
\(y-0 =-\frac{1}{2}(x - 8)\)
Simplify: \(y=-\frac{1}{2}x + 4\), which can be rewritten as \(y = 4-\frac{x}{2}\)

Answer:

\(y = 4-\frac{x}{2}\) (the option \(y = 4-\frac{x}{2}\))