Write the equation of a line passing through (4,7) with undefined (vertical) slope.
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A line with an undefined slope is vertical.
Therefore the equation will be in the form of x = #
The line passes through the point (4,7). The x-coordinate is 4.
Therefore the equation is x = 4
We have two things here, the slope and a point.
We'll start by worrying about the slope. The formula for the slope (m) is
`m =(Deltay)/(Deltax) = (y_(2) - y_(1))/(x_(2) - x_(1))`
See the link below to get some more information on slopes and how they work.
The only way the slope would be undefined is if the denominator were 0. If the denominator is 0, that means `x_(2)` and `x_(1)` are equal! It doesn't matter what y is, all the x's must be the same number.
Another way to thnk of this is that an undefined slope is a vertical line on a graph, like the one seen below:
Here, you see the graphed line is a vertical line. Because it is vertical, the x-value stays the same all the time. In this case, the x-value of every point on the line is 3. Therefore, the equation for this example line is:
In general, the form of an equation for a vertical line with be:
`x = a`
where "a' is simply a number.
Back to our problem:
We showed above that our line's equation will be of the form x = a, and we know that it goes through the point (4,7). We can recognize the equation of the line already.
Since we know the x-value (4) is the same number all the time, and we know that this number gives us the equation for the line, we get the equation below as the equation for our line:
To confirm, let's graph this equation and see if it both has an undefined slope and goes through (4,7):
As you can see, the point (4,7) is certainly on the line, and because the line is vertical, giving it an undefined slope. Our equation must therefore be:
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