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 grants path? $y = 2 - 4x$ $y = 4 - \frac{x}{2}$ $y = 6 - \frac{x}{4}$ $y = 8 - 2x$

Explanation:

Step1: Find the coordinates of points A and B

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

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 \((x_2,y_2)=(-4,6)\)

$$m=\frac{6 - 0}{-4 - 8}=\frac{6}{-12}=-\frac{1}{4}$$

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using point \(A=(8,0)\) and \(m =-\frac{1}{4}\)

$$y-0=-\frac{1}{4}(x - 8)$$

$$y=-\frac{1}{4}x+2$$

$$y = 6-\frac{x}{4}$$

(after re - arranging)

Answer:

\(y = 6-\frac{x}{4}\)