For this case we have that, by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutting point with the y axis
We have, according to the statement data that:
[tex]m = - \frac {2} {3}[/tex]
So, the equation is of the form:
[tex]y = - \frac {2} {3} x + b[/tex]
We also have that the line intersects the "x" axis at -3, that is, the line passes through the point [tex](x, y): (- 3,0)[/tex]
We substitute to find "b":
[tex]0 = -\frac {2} {3} (- 3) + b\\0 = -2 + b\\b = 2[/tex]
Finally, the equation is of the form:
[tex]y = - \frac {2} {3} x + 2[/tex]
Answer:
[tex]y = - \frac {2} {3} x + 2[/tex]
