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
We have the following points through which the line passes:
[tex](x_ {1}, y_ {1}): (- 3,2)\\(x_ {2}, y_ {2}) :( 5, -5)[/tex]
So the slope is:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-5-2} {5 - (- 3)} = \frac {-7} {5 + 3} = - \frac {7} {8}[/tex]
Thus, the equation of the line is of the form:
[tex]y = - \frac {7} {8} x + b[/tex]
We substitute one of the points and find "b":
[tex]2 = - \frac {7} {8} (- 3) + b\\2 = \frac {21} {8} + b\\b = 2- \frac {21} {8}\\b = \frac {16-21} {8}\\b = - \frac {5} {8}[/tex]
Finally, the equation is:
[tex]y = - \frac {7} {8} x- \frac {5} {8}[/tex]
Answer:
[tex]y = - \frac {7} {8} x- \frac {5} {8}[/tex]
