For this case we have that by definition, the equation of a line in the slope-intersection form is:
[tex]y = mx + b[/tex]
Where:
m: It is the slope
b: It is the cut point with the y axis
The slope is: [tex]m = \frac {2} {5}[/tex]
Thus, the equation is of the form:
[tex]y = \frac {2} {5} x + b[/tex]
We substitute the given point and find "b":
[tex]-5 = \frac {2} {5} (- 5) + b\\-5 = -2 + b\\-5 + 2 = b\\b = -3[/tex]
Finally, the equation is:
[tex]y = \frac {2} {5} x-3[/tex]
Answer:
[tex]y = \frac {2} {5} x-3[/tex]
