Question

What is the initial value of the function represented by this graph? 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 7, 5. 0 1 2 5 Question 7(Multiple Choice Worth 5 points)

Answer 1

Option 3 rd is correct

Initial value = 2

Explanation:

A equation of line is given by:

`y =mx+b` ....[1]

where

m is the slope of the line and b is the y-intercept or the initial value

As per the statement:

A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.

It is also given that:

A straight line joins the ordered pair (0, 2) with the ordered pair (7, 5)

Calculate slope:

using formula:

`\text{Slope (m)} = (y_2-y_1)/(x_2-x_1)`

Substitute the given ordered pairs we have;

`\text{Slope (m)} = (5-2)/(7-0)=(3)/(7)`

y-intercept states that the graph which cut y-axis.

Substitute x =0 and solve for x:

we have given with the ordered pair (0, 2)

⇒y-intercept(b) = 2

Substitute the given values of m and b in [1]

`y = (3)/(7)x+2`

The equation of straight line joins the ordered pair (0, 2) with the ordered pair (7, 5) is:

`y = (3)/(7)x+2`

The initial value of the function represented by the given graph as shown below is: 2

Answer 2

The initial value of the graph is 2. Third option is correct.

Explanation:

It is given that A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.

The line is passing through the points (0,2) and (7,5).

The point (0,2) is the y-intercept and graph labeled from 0 to 7, therefore 2 is the initial value.

Slope of line is

`m=(y_2-y_1)/(x_2-x_1)=(5-2)/(7-0)=(3)/(7)`

The equation of line is

`y=mx+b`

Where, m is slope and b is y-intercept. So the equation of given line is

`y=(3)/(7)x+2`

At initial condition the value of x is 0. So, put x=0.

`y=(3)/(7)(0)+2=2`

Therefore the initial value of the graph is 2. Option 3 is correct.