a circle representing a pool is graphed with a center at the origin. grant enters the pool at point a and…

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? $y = 2 - 4x$ $y = 4 - \\frac{x}{2}$ $y = 6 - \\frac{x}{4}$ $y = 8 - 2x$

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? $y = 2 - 4x$ $y = 4 - \\frac{x}{2}$ $y = 6 - \\frac{x}{4}$ $y = 8 - 2x$

Answer

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)