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 two points on the line

From the graph, assume two points \(A(8,0)\) and \(B(0,8)\) (by observing the x - intercept and y - intercept of the line representing Grant's path).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \(A(8,0)\) as \((x_1,y_1)\) and \(B(0,8)\) as \((x_2,y_2)\), we have \(m=\frac{8 - 0}{0 - 8}=\frac{8}{-8}=- 2\).

Step3: Use the slope - intercept form \(y=mx + b\)

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know \(m=-2\) and from point \(B(0,8)\), \(b = 8\). So the equation is \(y=-2x + 8\) or \(y = 8-2x\).

Answer:

\(y = 8-2x\) (the fourth option)