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 the slope formula

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. From the graph, point $A=(8,0)$ and point $B=(- 4,6)$.

Step2: Calculate the slope

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

Step3: Find the y - intercept

Using the point - slope form $y - y_1=m(x - x_1)$ with the point $A=(8,0)$ and $m =-\frac{1}{2}$, we have $y-0=-\frac{1}{2}(x - 8)$. Simplifying gives $y=-\frac{1}{2}x + 4$, or $y = 4-\frac{x}{2}$.

Answer:

$y = 4-\frac{x}{2}$ (corresponding to the second option in the multiple - choice list)