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 grant’s path? \\(\circ\\ y = 2 - 4x\\) \\(\circ\\ y = 4 - \frac{x}{2}\\) \\(\circ\\ y = 6 - \frac{x}{4}\\) \\(\circ\\ y = 8 - 2x\\)

Explanation:

Step1: Identify points A and B

From the graph, Point A is $(8, 0)$, Point B is $(-4, 6)$.

Step2: Calculate the slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{6-0}{-4-8}=\frac{6}{-12}=-\frac{1}{2}$

Step3: Find y-intercept (b)

Use point A $(8,0)$ in $y=mx+b$:
$0 = -\frac{1}{2}(8) + b$
$0 = -4 + b$
$b=4$

Step4: Form the equation

Substitute $m=-\frac{1}{2}$ and $b=4$ into $y=mx+b$:
$y = 4 - \frac{x}{2}$

Answer:

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