SOLUTION: what is the equation of the line that passes through the point (-4,7) and has an undefined slope?

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Question 1173444: what is the equation of the line that passes through the point (-4,7) and has an undefined slope?
Found 2 solutions by math_helper, Theo:
Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website!

Undefined slope ==> line is vertical ==> x = -4

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.

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