Question

1) Write an equation of the line that passes through the points.

Answer 1

1)

$\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad(\stackrel{x_2}{0}~,~\stackrel{y_2}{5})\\\\\\slope = m\implies\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-5}{0-2}\implies \cfrac{0}{-2}\implies 0\\\\\\\begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-5=0(x-2)\implies y-5=0\implies \boxed{y=5}$

2)

$\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{0})\qquad(\stackrel{x_2}{0}~,~\stackrel{y_2}{0})\\\\\\slope = m\implies\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-0}{0-(-3)}\implies \cfrac{0-0}{0+3}\implies \cfrac{0}{3}\implies 0\\\\\\\begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-0=0[x-(-3)]\\\\\\y=0(x+3)\implies \boxed{y=0}$

3)

$\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad(\stackrel{x_2}{4}~,~\stackrel{y_2}{-2})\\\\\\slope = m\implies\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-(-2)}{4-0}\implies \cfrac{-2+2}{4-0}\implies \cfrac{0}{4}\implies 0 \\\\\\\begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-(-2)=0(x-0)\implies y+2=0\implies \boxed{y=-2}$