Answer:
Equation of the line: [tex]y = -5[/tex].
Step-by-step explanation:
Let [tex](x_0,\, y_0)[/tex] and [tex](x_1,\, y_1)[/tex] denote the coordinates of these two points, respectively.
Calculate the slope [tex]m[/tex] of this line:
[tex]\displaystyle m = \frac{y_1 - y_0}{x_1 - x_0} = \frac{(-5) - (-5)}{8 - 0} = 0[/tex].
Notice that the slope is zero because the two points have the same [tex]y[/tex]-coordinates ([tex]y_0 = y_1 = -5[/tex]) even though their [tex]x[/tex]-coordinates are distinct ([tex]x_0 \ne x_1[/tex].)
Equation for this line in point-slope form:
[tex]y - y_0 = m\, (x - x_0)[/tex].
[tex]y - (-5) = 0\, (x - 0)[/tex].
Rewrite and simplify to obtain the equation of this line in slope-intercept form:
[tex]y = -5[/tex].
The [tex]x[/tex]-term was eliminated because the slope was zero.
