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contestada

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

Which equation represents Grants 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 f class=

Respuesta :

calculista

Answer:

[tex]y=4-\frac{x}{2}[/tex]

Step-by-step 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

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{6-0}{-4-8}[/tex]

[tex]m=\frac{6}{-12}[/tex]

[tex]m=-\frac{1}{2}[/tex]

step 2

Find the equation in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{1}{2}[/tex]

[tex]point\ A(8,0)[/tex]

substitute

[tex]y-0=-\frac{1}{2}(x-8)[/tex]

Convert to slope intercept form

[tex]y=mx+b[/tex]

Distribute in the right side

[tex]y=-\frac{1}{2}x+4[/tex]

rewrite

[tex]y=4-\frac{1}{2}x[/tex] -----> [tex]y=4-\frac{x}{2}[/tex]

Answer:

The correct option is B) [tex]y=4-\frac{x}{2}[/tex]

Step-by-step 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: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the respective values in the above formula.

[tex]m=\frac{6-0}{-4-8}[/tex]

[tex]m=\frac{6}{-12}[/tex]

[tex]m=-\frac{1}{2}[/tex]

Hence, the slope is [tex]-\frac{1}{2}[/tex]

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

The slope intercept form is: [tex]y=mx+c[/tex]

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

Substitute [tex]m=-\frac{1}{2}[/tex] and c=4 in slope intercept formula.

[tex]y=-\frac{1}{2}x+4[/tex]

[tex]y=4-\frac{x}{2}[/tex]

Hence, the correct option is B) [tex]y=4-\frac{x}{2}[/tex]