For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
[tex]y = mx+b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
According to the statement we have the following points:
[tex](x_ {1}, y_ {1}): (- 2, -4)\\(x_ {2}, y_ {2}): (- 3, -3)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-3 - (- 4)} {- 3 - (- 2)} = \frac {-3+4} {- 3+2} = \frac {1} {- 1} = - 1[/tex]
Thus, the equation is of the form:
[tex]y = -x + b[/tex]
We substitute one of the points:
[tex]-3 = - (- 3) + b\\-3 = 3 + b\\-3-3 = b\\b = -6[/tex]
Finally, the equation is of the form:
[tex]y = -x-6[/tex]
Answer:
[tex]y = -x-6[/tex]
