What is an equation of the line that goes through point (8, −9) and whose slope is undefined?

1 Answer
Zor Shekhtman
Nov 25, 2015

The equation of a line is x=8x=8.

Explanation:

General equation of a straight line on a coordinate plane is
ax+by+c=0ax+by+c=0
where aa, bb and cc - some real constants and variable xx and yy are coordinates.

In order for this line to go through point (8,-9)(8,−9), values x=8x=8, y=-9y=−9 should satisfy this equation:
a*8+b*(-9)+c=0a⋅8+b⋅(−9)+c=0

Since another condition is that a slope is undefined, it means that the line should be parallel to Y-axis, that is any other point with the same X-coordinate (x=8x=8) and any Y-coordinate (say, y=0y=0 or y=1y=1) also lies on this line and, therefore, should satisfy the equation.

For instance, let's use point (8,0)(8,0), which produces:
a*8+b*0+c=0a⋅8+b⋅0+c=0
And for point (8,1)(8,1):
a*8+b*1+c=0a⋅8+b⋅1+c=0
And any other point of a type (8,y)(8,y) should produce
a*8+b*y+c=0a⋅8+b⋅y+c=0

This necessitates b=0b=0 and the only condition on coefficients aa and cc is:
a*8+c=0a⋅8+c=0

Any real numbers that satisfy the above conditions, for instance a=1, c=-8a=1,c=−8 or a=2, c=-16a=2,c=−16 etc., are good to be coefficients to construct an equation of a line that goes through point (8,-9)(8,−9).

Examples are:

  1. a=1, b=0, c=-8a=1,b=0,c=−8
    Equation: x-8=0x−8=0

  2. a=2, b=0, c=16a=2,b=0,c=16
    Equation 2x-16=02x−16=0

Obviously, all equations are equivalent to each other and can be reduced to a form x=8x=8.

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