The slope is defined as the ratio between the difference of the yy components and the difference of the xx components of a given pair of points on a line.
In other words, given a line, pick two points P_1 = (x_1,y_1)P1=(x1,y1) and P_2 = (x_2,y_2)P2=(x2,y2), the slope mm is defined as
m = \frac{y_2-y_1}{x_2-x_1}m=y2−y1x2−x1
In your case, the line x=7x=7 is composed, as the equation suggests, by all the points having the xx component equal to 77, and any yy component. So, two points on the line have the form P_1 = (7,y_1)P1=(7,y1) and P_2 = (7,y_2)P2=(7,y2)
Can you see the problem? If we compute the slope, we have
m = \frac{y_2-y_1}{x_2-x_1} = \frac{y_2-y_1}{7-7} = \frac{y_2-y_1}{0}m=y2−y1x2−x1=y2−y17−7=y2−y10
And you can't divide by zero. This is the reason why all vertical lines (i.e. those with equation x=kx=k, for some real number kk) have no defined slope.
