To fins the linear equation you shoul use two of the points to find the slope
a=(-2,6) b=(4,9)
and use the formula for the slope in this way

after you have the slope you can use whichever point you want to find b
y=mx+b
lets use point (-2,6)

the equation should be

to check if the answer is correct we can replace in the equation with one of the point; lets use (-4,5)

with this we can conclude the equation is correct.