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}) :( 8,5)\\(x_ {2}, y_ {2}): (- 6,5)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {5-5} {- 6-8} = \frac {0} {- 14} = 0[/tex]
The slope is zero.
Thus, the equation is of the form:
[tex]y = b[/tex]
We substitute one of the points and find b:
[tex](x, y) :( 8,5)\\5 = b\\b = 5[/tex]
Finally, the equation is:
[tex]y = 5[/tex]
Answer:
[tex]y = 5[/tex]
