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's the slope
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}) :( 1,3)\\(x_ {2}, y_ {2}): (- 3, -5)[/tex]
We found the slope:
[tex]m = \frac{y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Substituting we have:
[tex]m = \frac {-5-3} {- 3-1} = \frac {-8} {- 4} = 2[/tex]
Thus, the equation is of the form:
[tex]y = 2x + b[/tex]
We substitute one of the points and find the cut-off point:
[tex]3 = 2 (1) + b\\3 = 2 + b\\3-2 = b\\b = 1[/tex]
Finally, the equation is:
[tex]y = 2x + 1[/tex]
ANswer:
[tex]y = 2x + 1[/tex]
