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
is given by

Slope for points (-9,-2) and (-5,-7) is
=

=

Equation is given by:

which is a linear equation.
The model of the given linear equation is attached.