Question

Choose the equation of the horizontal line that passes through the part point (1,-5)

Answer 1

We know is a horizontal line, so, if it passes through 1,-5, it also passes through "whatever", -5, like 20, -5 or 1000000, -5, or -100000000, -5 and so on.

so, let's pick another point say -7, -5, check the picture below, and let's check about the equation that runs through it,

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 1 &,& -5~) % (c,d) &&(~ -7 &,& -5~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-(-5)}{-7-1} \\\\\\ \cfrac{-5+5}{-7-1}\implies \cfrac{0}{-8}\implies 0 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-5)=0(x-1) \\\\\\ y+5=0\implies y=-5$

Answer 2

The answer is A. Y=-5