For this case we have that by definition, the equation of the line in 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 two points through which the line passes:
[tex](x_ {1}, y_ {1}) :( 5, -1)\\(x_ {2}, y_ {2}) :( 4, -5)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-5 - (- 1)} {4-5} = \frac {-5+ 1} {- 1} = \frac {-4} {- 1} = 4[/tex]
Thus, the equation is of the form:
[tex]y = 4x + b[/tex]
We substitute one of the points and find b:
[tex](x,y):(5,-1)\\-1=4(5)+b\\-1=20+b\\-1-20=b\\b=-21[/tex]
Finally, the equation is:
[tex]y = 4x-21[/tex]
Answer:
[tex]y = 4x-21[/tex]
