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 assume point \(B=(0,4)\) (since we need two - point form of a line. If we assume another point on the line, we can also calculate, but from the options and the intercept - like form \(y = mx + b\) where \(b\) is the \(y\) - intercept).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \(A=(x_1,y_1)=(8,0)\) and \(B=(x_2,y_2)=(0,4)\), we have \(m=\frac{4 - 0}{0 - 8}=-\frac{1}{2}\).

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 found \(m =-\frac{1}{2}\) and from point \(B=(0,4)\), \(b = 4\).
Substituting \(m\) and \(b\) into the formula \(y=mx + b\), we get \(y=4-\frac{1}{2}x\)

Answer:

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