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?


y = 2 – 4x

y = 4 – X over 2

y = 6 – X over 4

y = 8 – 2x

Answer 1

Answer:

The equation of Grant's path is y = 4 - x over 2 ⇒ 2nd answer

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

• m is the slope of the line
• b is the y-intercept (value y at x = 0)

The formula of the slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ Grant's path is a line from point A to point B

∴ The equation of AB represents Grant's path

Lets find the slope of AB using the formula of the slope above

∵ A = (8 , 0)

∵ B = (-4 , 6)

∴ $x_{1}$ = 8 and $x_{2}$ = -4

∴ $y_{1}$ = 0 and $y_{2}$ = 6

∵ $m=\frac{6-0}{-4-8}=\frac{6}{-12}$

∴ $m=-\frac{1}{2}$

Substitute the value of m in the form of the equation

∵ y = m x  + b

∴ y = $-\frac{1}{2}$ x + b

∵ b is the value of y at x = 0

∵ y = 4 at x = 0 ⇒ from the figure

∴ b = 4

∴ y = $-\frac{1}{2}$ x + 4

We can write $-\frac{1}{2}$ x as $-\frac{x}{2}$

∴ y =  $-\frac{x}{2}$ + 4

- Switch the two terms of the right hand side

∴ y = 4 -  $\frac{x}{2}$

The equation of Grant's path is y = 4 -  $\frac{x}{2}$