Question 85100: hi, how would I be able to find an equation of the line through the point (-2/3, 1)with undefined slope? What process will I use?
Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find an equation of the line through the point (-2/3, 1)with undefined slope?
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If the slope is undefined the equation looks like x=k
But your line passes thru x=-2/3
So, the equation must be x=-2/3
It passes thru all points where x=-2/3
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Cheers,
Stan H.
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! The undefined slope is the clue. It tells you that the graph is a vertical line. Why so?
Because the slope will always have a real value as long as there is a change in x. Recall
that the slope is defined as:
.
.
But if the run (horizontal change or change in x) is zero, the slope is undefined
because in algebra division by zero is not allowed.
.
Therefore, we know the horizontal change in the graph is zero. So the graph shows that no
matter what the value of y is, x always has to be the same because it cannot change.
.
Now the question is where would the vertical line be. Well, since it has to go up through
the y value of 1, it must have the x value that corresponds to the y value of 1. The problem
tells you that the x corresponding x value is -2/3.
.
So the graph you are looking for is a vertical line that goes through -2/3 on the x axis
and therefore, it goes through 1 in the y direction as well as lots of other y values in
both the positive and negative direction. The equation for this line is x = -2/3.
There is no y in the equation at all because y can be any value, but x always has to
be -2/3 so that the line will go up through the value of y = 1.
.
Hope this helps you to understand the problem and its answer a little better.
.
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