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 \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \((x_1,y_1)=(8,0)\) and \((x_2,y_2)=(-4,6)\) into the formula:

$$m=\frac{6 - 0}{-4 - 8}=\frac{6}{-12}=-\frac{1}{2}$$

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

Use point \(A=(8,0)\) and \(m =-\frac{1}{2}\)

$$y-0=-\frac{1}{2}(x - 8)$$

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

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

Answer:

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