Question

What is the equation of the line that has a slope of 0 and passes through the point (6,-8)

Answer 1

Answer: Hello there!

we want to find the equation that passes through the point (6, -8) (where this notation stands for (x,y)) with a slope of 0.

a linear equation has the form y = ax+ b

where a is the slope and b is the intercept.

if a = 0, our equation has the form y = b (has no dependence of x)

so we have a constant equation that passes through the point (6, -8) , this means x = 6 and y = -8, but we know that y is constant:

then y = -8 = b

so our equation is y(x) = -8

Answer 2

$\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=0(x-6)\implies y+8=0\implies y=-8$