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? o y = 2 - 4x o y = 4 - \\(\\frac{x}{2}\\) o y = 6 - \\(\\frac{x}{4}\\) o 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? o y = 2 - 4x o y = 4 - \\(\\frac{x}{2}\\) o y = 6 - \\(\\frac{x}{4}\\) o y = 8 - 2x

Answer

Answer:

y = 8 - 2x

Explanation:

Step1: Encontrar dos puntos en la recta

Los puntos A(6, - 4) y B(-2, 20) están en la recta que representa el camino de Grant.

Step2: Calcular la pendiente (m)

La fórmula de la pendiente es $m=\frac{y_2 - y_1}{x_2 - x_1}$. Sustituyendo $x_1 = 6,y_1=-4,x_2=-2,y_2 = 20$: $m=\frac{20-(-4)}{-2 - 6}=\frac{24}{-8}=-2$

Step3: Encontrar la ecuación de la recta en forma pendiente - intersección (y = mx + b)

Usamos el punto A(6, - 4) y $m=-2$. Sustituimos en $y=mx + b$: $-4=-2\times6 + b$ $-4=-12 + b$ $b=-4 + 12=8$ La ecuación de la recta es $y=-2x + 8$, es decir $y = 8 - 2x$.