This is a linear function because there are constant differences between the y values and the x values. The (x,y) values are effectively points on the line. We need to find the slope and y intercept.
Any two sets of x-y values will give us the slope so let’s pick the first pair of coords: (-3-(-4))/(-2-(-5))=(-3+4)/(-2+5)=⅓ so y=⅓x+b where b is the y intercept.
Plug the first point (-2,-3) into this equation: -3=-⅔+b, so b=⅔-3=-7/3 and y=⅓x-7/3=⅓(x-7), which can be written 3y=x-7.
CHECK: Now put x=1, 3y=1-7=-6 so y=-2 which is (1,-2) and this appears in the list. Now put x=4, 3y=4-7=-3, so y=-1 and (4,-1) also appears in the list, confirming the equation. We can write this as f(x)=⅓x-7/3, or we can use the inverse which is x=3y+7, which we can write as g(y)=3y+7. Since y is only a place holder, we can write this as y=g(x)=3x+7, which means the coords in the list are (y,x) values instead of (x,y).