Question

Use the table to answer the question.

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

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

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

$y-(-1)=\dfrac{1-(-1)}{0-(-1)}(x-(-1))$

$y+1=\dfrac{1+1}{0+1}(x+1)$

$y+1=\dfrac{2}{1}(x+1)$

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

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.