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 - x/2, y = 6 - x/4, y = 8 - 2x

Explanation:

Step1: Identify points A and B

From the graph, point A is at \((8, 0)\) and point B is at \((-4, 6)\) (by reading the coordinates from the grid).

Step2: Calculate the slope (m)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(8,0)\) and \((x_2,y_2)=(-4,6)\). Then \(m=\frac{6 - 0}{-4 - 8}=\frac{6}{-12}=-\frac{1}{2}\).

Step3: Use point - slope form to find the equation

Using point A \((8,0)\) and slope \(m = -\frac{1}{2}\), the point - slope form is \(y - y_1=m(x - x_1)\). Substituting values: \(y - 0=-\frac{1}{2}(x - 8)\). 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 \(y = 4-\frac{x}{2}\))