Answer:
[tex]\displaystyle y=-7x-5[/tex]
Step-by-step explanation:
Equation of the Line
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
We'll take the first two points (-2,9) and (-1,2)
[tex]\displaystyle y-9=\frac{2-9}{-1+2}(x+2)[/tex]
Operating:
[tex]\displaystyle y-9=\frac{-7}{1}(x+2)[/tex]
[tex]\displaystyle y-9=-7(x+2)[/tex]
[tex]\displaystyle y-9=-7x-14[/tex]
Adding 9:
[tex]\boxed{\displaystyle y=-7x-5}[/tex]
Substituting the last two points we can verify they also belong to the line.
