Question 1173444
an undefined slope means that the line is vertical.


if the line is vertical, then the equation is x = -4


the value of x is -4 and there are an infinite number of values of y that satisfy the equation, (-4,7) being one of them.


consider the equation for the slope of the line.


the slope is equal to (y2 - y1) / (x2 - x1).


if (x2 - x1) is equal to 0, then the slope is undefined.


if (x2 - x1) is equal to 0, then x2 must be equal to x1.


this means that you have a different value of y for the same value of x.


this can only occur if the line is perpendicular.


if the line is perpendicular, then the equation becomes x = c


c can be any constant.


this means that there are an infinite number of possibilities for the value of y.


here's a graph with a couple of examples of points that are on the line.


<img src = "http://theo.x10hosting.com/2021/012101.jpg" >


you can see that there are multiple values of y for the line x = -4, with y = 7 being one of them.