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 point with the y axis
We have the following points:
[tex](x_ {1}, y_ {1}) :( 5, -5)\\(x_ {2}, y_ {2}) :( 4,0)[/tex]
We find the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0 - (- 5)} {4-5} = \frac {5} {- 1} = - 5[/tex]
Thus, the equation is of the form:
[tex]y = -5x + b[/tex]
We substitute a point and find b:
[tex]0 = -5 (4) + b\\0 = -20 + b\\b = 20[/tex]
Finally, the equation is:
[tex]y = -5x + 20[/tex]
Answer:
[tex]y = -5x + 20[/tex]
