Write an Equation That Represents the Linear Relationship Between the Variables in the Table

Let y = ax+b

Letting (x, y) = (0, 7), we obtain the equation a(0)+b=7, or b= 7

Letting (x, y) =(1, 2), we obtain the equation a+7=2, or a= -5

Thus, the equation is y= -5x + 7

the linear  equation   y = mx +b

relationship between the variables in the table.

m =   (y_{2 -} y₁)  / (x₂ - x₁) =  (2-7) / (1-0)  ,  m = - 5,

    then  y =  -5x +b

find b : value from table : y = 7, x = 0

7 = -5(0) + b 

b = 7

Then  an equation that represents the linear relationship between the variables in the table.

y = -5x +7