Answer:
[tex]y = 17[/tex].
Step-by-step explanation:
In general, the equation of a line in a cartesian plane may be written as [tex]y = m\, x + b[/tex], where [tex]m[/tex] and [tex]b[/tex] are constants: [tex]m\![/tex] is the slope of this line, and [tex]b\![/tex] is the [tex]y[/tex]-intercept of this line.
A point [tex](x_{0},\, y_{0})[/tex] is on a given line if and only [tex]x := x_{0}[/tex] and [tex]y := y_{0}[/tex] (setting [tex]x[/tex] to [tex]x_{0}[/tex] and [tex]y[/tex] to [tex]y_{0}[/tex]) would satisfy the equation of that line.
That is: [tex]y_{0} = m\, x_{0} + b[/tex].
A line in a cartesian plane is horizontal if and only if its slope is [tex]0[/tex]. That is: [tex]m = 0[/tex]. The equation of this line would be in the form [tex]y = b[/tex] for some constant [tex]b[/tex].
The point [tex](-5,\, 17)[/tex] is on the line in this question. Thus, [tex]x := -5[/tex] and [tex]y := 17[/tex] should satisfy the equation of this line. That is: [tex]17 = b[/tex].
Hence, the value of the constant [tex]b[/tex] would be [tex]17[/tex] for this particular line. The equation of the line would be [tex]y = 17[/tex].
