Question

Find the equation of the line that passes through the given points. Include your work in your final answer. (5, 4) and (5, 6)

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 5}}\quad ,&{{ 4}})\quad % (c,d) &({{ 5}}\quad ,&{{ 6}}) \end{array} \\\quad \\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}} \\ \quad \\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\ \left.\qquad \right.\uparrow\\ \textit{point-slope form}$

Answer 2

This would be a line that goes straight up and down and could be written as

x=5

As far as showing work goes. I used my back knowledge that for two points to be on the same line and share either their x or y-coordinates, it is either a vertical or a horizontal line.

Vertical if the x's are the same
Horizontal if the y's are the same