The y intercept is -2 and the slope is -2/3 so the vertex form of this equation should be
y = -2/3 x -2
Standard form is x + y = number
We have to move x onto the other side
2/3 x + y = -2
The coefficient before x cannot be a fraction or negative so you have to multiply the whole equation by 3
2x + 3y = -6
