For this case we have that by definition, the equation of a line of 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
The slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
We have that the line m passes through the following points:
[tex](x_ {1}, y_ {1}): (-3,3)\\(x_ {2}, y_ {2}): (-4, -6)[/tex]
So, the slope of the line m is:
[tex]m = \frac {-6-3} {- 4 - (- 3)} = \frac {-9} {- 4 + 3} = \frac {-9} {- 1} = 9[/tex]
Line n has the same slope so the equation is of the form:
[tex]y = 9x + b[/tex]
We have as data that the y-intercept is [tex]-\frac{2} {3}[/tex]. Thus, we have that the equation of line n is:
[tex]y = 9x- \frac {2} {3}[/tex]
ANswer:
[tex]y = 9x-\frac {2} {3}[/tex]
