The best way to assess a function when they give us the (x, y) pairs, is by plotting them.
I am adding below a plot of the data points (just give me a few seconds for the drawing to complete)
We can see that indeed the plotted values form a line, therefore there is a linear equation that represents this relationship.
Notice that the "slope" of the line will result as a negative value, and also the y-intercept will be negative.
We use any two pair of points to find the slope:
for example the points (-2, 4) and (1, -5)
slope = (y2 - y1) / (x2 - x1)
in our case:
slope = (-5 - 4) /(1 - -2) = -9 / 3 = -3
The slope is -3 and we can use now the point-slope form of a line to find the equation:
y - y1 = m (x - x1)
y - 4 = -3 (x - -2)
y - 4 = -3 (x + 2)
y - 4 = -3 x - 6
add 4 to both sides:
y = - 3 x - 2
This is the equation of the line in slope-intercept form.