For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut-off point with the y axis.
According to the data of the statement we have the following points:
[tex](x_ {1}, y_ {1}): (- 9, -9)\\(x_ {2}, y_ {2}): (- 6,0)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0 - (- 9)} {- 6 - (- 9)} = \frac { 9} {- 6 + 9} = \frac {9} {3} = 3[/tex]
Thus, the equation is of the form:
[tex]y = 3x + b[/tex]
We substitute one of the points and find b:
[tex]0 = 3 (-6) + b\\0 = -18 + b\\b = 18[/tex]
Finally, the equation is:
[tex]y = 3x + 18[/tex]
Answer:
[tex]y = 3x + 18[/tex]
