Question 214797
We are presently graphing linear equations.  I am totally lost.  We have to anwer a response to:  Why the line x=4 is a vertical line? How do begin? How do I solve this?


Step 1.  A line is given in slope-intercept form as y=mx+b where m is the slope and b is the y-intercept at point (0,b).  The y-intercept intersects the y-axis when x=0.  When we substitute x=0  into y=mx+b we get y=b.  So the point (0,b) is a point in the line.   Another point in the line is when y=0 then 0=mx+b or x=-b/m.


Step 2.  Now, why is the line vertical for x=4.  Note y can be any value as long as it has it's x-coordinate to be 4.

For example,  consider the the points (4, 0), (4, 1), and (4, -1) plot it in the graph and draw a line through these points.   What all these points have in common is that they have the x-coordinate to be 4.  In fact, you can have many y-values with an x-coordinates of 4 or x=4.


Now if y=4, then you have many points with y-coordinate of 4.  That is, points (0,4), (-1,4) and (1,4) will have the same y=4 and different values of x.  When you plot these points then these points, the line will be horizontal.



I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J