Yes, the given relationship shown by the data is linear, as the values of x variables vary with a difference of 4 and all the values of y variables vary with a difference of -5.
The slope(m) of for the points [tex] (x_{1},y_{1}) and (x_{2},y_{2}) [/tex] is given by [tex] \frac{(y_{2}-y_{1}) }{(x_{2}-x_{1})} [/tex]
Slope for points (-9,-2) and (-5,-7) is
= [tex] \frac{(-7+2) }{(-5+9)} [/tex]
=[tex] \frac{-5 }{4} [/tex]
Equation is given by: [tex] (y-y_{1})= m(x-x_{1}) [/tex]
[tex] 4y+5x=-53 [/tex] which is a linear equation.
The model of the given linear equation is attached.
