Question

Find the slope of the line through the points (5,1) and (5,3). Slope is 0 Slope is 5 Slope is 2 Undefined slope

Answer 1

The two points we have are:

$(5,1)\text{ and }(5,3)$

To calculate the slope between any two points, we use the slope formula "m":

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

Where m is the slope, and the points are (x1,y1) and (x2,y2).

We need to label our points as follows:

$\begin{gathered} x_1=5 \\ y_1=1 \\ y_2=5 \\ y_2=3 \end{gathered}$

And we substitute these values into the slope formula:

$m=\frac{3-1}{5-5}$

Solving the operations:

$m=\frac{2}{0}$

It is important to note that we have a 0 in the denominator, this is an indication of an undefined slope.

Undefined slopes occur when the line between the two points is a vertical line, and it is represented by having a 0 in the denominator when we calculate the slope.

Answer: Undefined slope