how can I find the equation of a line that passes through (-4,-8) and has undefined slope?

Question

The topic of this problem is "Use the Point-slope Equation of a line.

Answer 1

  Vertical lines have slope undefined;

 

    Because all points on vertical lines have the same value as X coordinate, Say K

 

     Therefore m =ΔY/ΔX =  ΔY/( K - K) = ΔY/ 0  , which is undefined.

 

   In this case k = -8

 

     All points : ( - 4 , -8) , ( -4, 256)  ( -4 , -37) , ........

 

      The equation of line is  X = -4 , for all values of Y

Answer 2

Hi Justin;

POINT-SLOPE EQUATION is....
y-y₁=m(x-x₁)
m is herein undefined.

Slope, m, is defined as change-of-y divided by change-of-x...

m=(y-y₁)/(x-x₁)

The mathematical concept of undefined means that the denominator is zero.  This means that both values of x are equal.

(-4,-8)

This equation is x=-4

It is a vertical line and includes the point of y=-8.

 

Answer 3

If the slope is undefined, it means that it is a vertical line.  This means that it passes through all points in the y direction.  Since the x value is -4, and the line is vertical, that's the only x value on that line.  So you just say the equation of the line is x=-4