through (2,5) slope = underfined

Question

show me how to write the slope intercept form of the equation of the line through the given point with the given slope. through (2,5) slope = underfined

Answer 1

The answer is not y=5.  But it is a vertical line.

 

A vertical line goes up and down.

in other words, it is perpendicular to the x axis.

 

Slope can be understood as rise/run.  It is the change in y (vertical (up/down)) per (or for each) change in x (horizontal (across)).

 

 

When it says slope is undefined - that comes from the fact that you get slope by dividing rise by run.  You cannot divide by 0. It simply is a concept undefined in all of math.  So they say the slope is undefined when you get a "run" of zero. 

 

This line in your problem goes through (2,5).  It has an undefined slope - meaning the rise can be anything, but the run is 0.  The line goes straight up and down.  You will see the line goes through the the x axis at x = 2.

 

It is a bit of a trick to ask the line be written in slope intercept form.  The slope is undefined, AND there is no y intercept.  There is no y=mx+b that fits in this situation.

 

The equation of this line is x=2. An equation like that is saying - I don't care what y value you give me, the x value is 2.  For ANY y.  Therefore y does not appear in the equation.  Because the y doesn't matter.  X=2 ALWAYS, for every y.

 

Answer 2

A vertical line has an undefined slope.  For a vertical line, the value of x is a constant.  The equation of the line is:

      x=2     (y may be any value)

Answer 3

You should know that a vertical line has an undefined slope.

 

y = 5