Question

Table

2
4
6
8
10
y
3 5 7 9 11
The data in the table is MOST closely modeled by graph

Answer 1

The graph of the the equation
`\:y=x+1` is also attached below.

Explanation:

Here is the given table

x y

2 3

4 5

6 7

8 9

10 11

Taking any two points:

• (2, 3)

• (4, 5)

`\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(2,\:3\right),\:\left(x_2,\:y_2\right)=\left(4,\:5\right)`

`m=(5-3)/(4-2)`

`m=1`

As the slope-intercept form is given by

`y\:=\:mx+b`

Plugging any point, let say (2, 3) and m = 1 in the slope-intercept form to get the value of 'b' (y-intercept).

`y\:=\:mx+b`

`3\:=\:\left(1\right)2+b`

`\mathrm{Switch\:sides}`

`\left(1\right)\cdot \:2+b=3`

`2+b=3`

`\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}`

`2+b-2=3-2`

`b=1`

So the equation for the data presented in table will be:

`y\:=\:mx+b`

• m = 1

• b = 1

Plugging the values in the equation

`y\:=\:mx+b`

`y\:=\:\left(1\right)x+1`

`\:y=x+1`

Where

the slope = m = 1

y-intercept = b = 1

The graph of the the equation
`\:y=x+1` is also attached below.