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

Explanation:

Step1: Find two - point form

The two points are \(A(8,0)\) and \(B(- 4,6)\). The slope \(m\) of the line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_1 = 8,y_1 = 0,x_2=-4,y_2 = 6\), so \(m=\frac{6 - 0}{-4 - 8}=\frac{6}{-12}=-\frac{1}{2}\).

Step2: Use point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\). Using point \(A(8,0)\) and \(m =-\frac{1}{2}\), we have \(y-0=-\frac{1}{2}(x - 8)\).

Step3: Simplify the equation

Expand the right - hand side: \(y=-\frac{1}{2}x + 4\), which can be written as \(y = 4-\frac{x}{2}\).

Answer:

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