Question

(05.03 LC)

What is the initial value of the function represented by this graph? (1 point)

A coordinate grid is shown with x- and y-axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 2 with the ordered pair 5, 0.

0

2

3

5

Answer 1

2, two, duos

Explanation:

Answer 2

2

Explanation:

Let's find the function first. We know that the function join the points (0, 2) and (5, 0) with a line, so we have a linear function. We need to find the slope of the line joining those two points using the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

where

`m` is the slope of the line

`(x_1, y_1)` are the coordinates of the first point

`(x_2,y_2)` are the coordinates of the second point

Our first point is (0, 2), so
`x_1=0` and
`y_1=2`; our second point is (5, 0), so
`x_2=5` and
`y_2=0`. Replacing the values:

`m=(y_2-y_1)/(x_2-x_1)`

`m=(0-2)/(5-0)`

`m=(-2)/(5)`

`m=-(2)/(5)`

Now that we have the slope of our line, we can use the point-slope formula to complete our function:

`y-y_1=m(x-x_1)`

where

`m` is the slope

`(x_1,y_1)` are the coordinates of the first point

Replacing values:

`y-2=-(2)/(5)(x-0)`

`y-2=-(2)/(5) x`

`y=-(2)/(5) x+2`

`f(x)=-(2)/(5) x+2`

Now, the initial value of our function is the value at
`x=0`, so:

`f(0)=-(2)/(5) (0)+2`

`f(0)=2`

We can conclude that the initial value of the function is 2.