Why is there no x in the equation of a horizontal line? why is there no y in the equation of a vertical line?

Question

Still don't understand after class. 

Answer 1

The Slope-intercept form of the equation of a line is: 

     y = mx + b     where m=slope and b=y-intercept

 

If the slope m=0, then the line is horizontal and can be represented as:  y=b

   So, these are all horizontal lines:

           y=0    {the x-axis)

           y=5

           y=7

    Note that y has a constant value for any value of x.

 

The Slope-intercept form of the equation of a line cannot represent a vertical line because the slope m is undefined.

Thus, we use the Standard Form of the equation of a line:

     Ax + By = C

 

For a vertical line, the value of B=0, so the line can be represented as:   x=C/A   (A and C are both constants)

   So, these are all vertical lines:

           x=0    (the y-axis)

           x=3

           x=4

 

In English:

      A horizontal line has a constant value of y for any possible value of x.

      A vertical line has a constant value of x for any possible value of y.

Answer 2

In the case of a horizontal line, there is no slope. Imagine a horizontal line y = 5.

If x = 0, then y = 5.

If x = 7, y = 5.

If x = 2,135,342,568,245,129,482,547, y still equals 5.

Look at the slope-intercept formula y = mx + b. When we have no slope, that means m = 0, and as we learned in basic multiplication, anything times 0 equals 0.

So if m = 0, then 0 times x is also 0. This ends up relegating x as a 0 as well, meaning there is no x.

(y = 0x + 5 becomes y = 5)

 

Now for a horizontal line. This may be trickier to explain. Here we have x = 5. The only viable point on the graph is the spot 5 on the graph. Is it ever 4? no. Is it ever 6? no. Is it ever 5.00000000000000000000001? No. But every point of y is defined when x = 5. Y can be any number and is every number because x=5 is true.

 

Another way to think would be that if x = 5 is true, then y can be any and every possible number. If x ≠ 5, then there is no y-value possibility and thus no possible number.