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
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
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
[tex]y-(-1)=\dfrac{1-(-1)}{0-(-1)}(x-(-1))[/tex]
[tex]y+1=\dfrac{1+1}{0+1}(x+1)[/tex]
[tex]y+1=\dfrac{2}{1}(x+1)[/tex]
[tex]y+1=2(x+1)[/tex]
Using distributive property, we get
[tex]y+1=2(x)+2(1)[/tex]
[tex]y+1=2x+2[/tex]
Subtracting 1 from both sides, we get
[tex]y+1-1=2x+2-1[/tex]
[tex]y=2x+1[/tex]
Therefore, the required equation is [tex]y=2x+1[/tex]. Hence, the correct option is D.
