Question

Graph the line passing through the given point with the given slope

$25. \text{(3,-2),undefined}$

Short answer

The graph of the line passing through the point $(3,-2)$ with the undefined slope is

Step-by-step solution

Step-1 – Apply the concept of slope of a line

The slope of a line is the ratio of the change in the y-coordinates to the change in the x- coordinates.

Symbolically, the slope m of the line passing through the points $\left(x_1,y_1\right)\text{and}\left(x_2,y_2\right)$is given by $m=\frac{y_2-y_1}{x_2-x_1}$where $x_1\ne x_2$.

Step-2 – Plot the given ordered pair   

The given ordered pair is $\left(3,-2\right)$

Hence plot the point in the graph such that the point is 3 unit in the positive x-axis and 2 units in the negative y-axis.

Therefore, the point $\left(3,-2\right)$ in the graph is as shown below:

Step-3 – Find a new point using the slope

Given that the slope is undefined.

Slope is said to be undefined only when the denominator in $m=\frac{y_2-y_1}{x_2-x_1}$is zero (i.e) only when $x_2-x_1=0\Rightarrow x_2=x_1$. If a slope is undefined then the line will be vertical and hence the line passes through the same value of xand different values of y. That is the value of x remains 3 through the line.

Step-4 – Graph the line

Draw a line passing through the point $\left(3,-2\right)$and parallel to $x=3$.