Question

Which equation represents Grant's path?

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.
O
y= 2 - 4x
O y=4-
O
y = 6-
0
Oy = 8 - 2x
-10
to
22
4
6
10
x

Answer 1

The correct option is B)
`y=4-(x)/(2)`

Explanation:

Consider the provided graph.

The coordinates of A is (8,0)

The coordinates of B is (-4,6)

First find the slope of the line by using the formula:
`m=(y_2-y_1)/(x_2-x_1)`

Substitute the respective values in the above formula.

`m=(6-0)/(-4-8)`

`m=(6)/(-12)`

`m=-(1)/(2)`

Hence, the slope is
`-(1)/(2)`

Now consider the graph, from the graph we know the y intercept of the line is (0,4).

The slope intercept form is:
`y=mx+c`

Where, m is the slope of line and c is the y intercept.

Substitute
`m=-(1)/(2)` and c=4 in slope intercept formula.

`y=-(1)/(2)x+4`

`y=4-(x)/(2)`

Hence, the correct option is B)
`y=4-(x)/(2)`

Answer 2

`y=4-(x)/(2)`

Explanation:

Find the coordinates of point A and point B

Looking at the graph

we have the points

A(8,0) and B(-4,6)

step 1

Find the slope m

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(6-0)/(-4-8)`

`m=(6)/(-12)`

`m=-(1)/(2)`

step 2

Find the equation in point slope form

`y-y1=m(x-x1)`

we have

`m=-(1)/(2)`

`point\ A(8,0)`

substitute

`y-0=-(1)/(2)(x-8)`

Convert to slope intercept form

`y=mx+b`

Distribute in the right side

`y=-(1)/(2)x+4`

rewrite

`y=4-(1)/(2)x` ----->
`y=4-(x)/(2)`