Question

Use the table to answer the question.

x
y
-1 -1
0 1
1
3
2
5
Which equation best models the relationship shown in the table?
O A. y = x - 1
O B. y = x + 1
OC. y = 2x – 1
d
D. y = 2x + 1

Answer 1

Given:

The table of values of a linear relationship.

x y

-1 -1

0 1

1 3

2 5

To find:

The equation for the given table of values.

Solution:

If a linear function passes through the two points, then the equation of the linear relationship is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Consider any two point from the given table. Let the two points are (-1,-1) and (0,1). So, the equation of the linear relationship is

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

`y+1=(1+1)/(0+1)(x+1)`

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

`y+1=2(x+1)`

Using distributive property, we get

`y+1=2(x)+2(1)`

`y+1=2x+2`

Subtracting 1 from both sides, we get

`y+1-1=2x+2-1`

`y=2x+1`

Therefore, the required equation is
`y=2x+1`. Hence, the correct option is D.