Question

write the equation of the line that passes through the points (5,-9) and (5,8) put your answer in fully reduced point-slope form unless it is a vertical or horizontal line

Answer 1

The point-slope form of the equation of a line is given as per below;

$y-y_1=m(x-x_1)$

where m = slope.

Let's go ahead and find the slope of the line using the below equation;

$m=\frac{y_2-y_1}{x_2-x_1}$

From the question, we know that x1 = 5, x2 = 5, y1 = -9 and y2 = 8.

So let's substitute these values into the above equation and find the slope;

$\begin{gathered} m=\frac{8-(-9)}{5-5} \\ m=\frac{8+9}{0} \\ m=\frac{17}{0} \\ \therefore m=\text{undefined} \end{gathered}$

We can see that the slope of the line is undefined. So it means that the line is a vertical line because x2-x1 = 0.

Our equation will now be y = -9

NB: Vertical lines always have undefined slope while horizontal lines always have their slope to be equal to zero.