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

Question

Sophia Alfred · Accepted Answer

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

General equation of a straight line on a coordinate plane is #ax+by+c=0# where #a#, #b# and #c# - some real constants and variable #x# and #y# are coordinates. In order for this line to go through point #(8,-9)#, values #x=8#, #y=-9# should satisfy this equation: #a*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=8#) and any Y-coordinate (say, #y=0# or #y=1#) also lies on this line and, therefore, should satisfy the equation. For instance, let's use point #(8,0)#, which produces: #a*8+b*0+c=0# And for point #(8,1)#: #a*8+b*1+c=0# And any other point of a type #(8,y)# should produce #a*8+b*y+c=0# This necessitates #b=0# and the only condition on coefficients #a# and #c# is: #a*8+c=0# Any real numbers that satisfy the above conditions, for instance #a=1, c=-8# or #a=2, c=-16# etc., are good to be coefficients to construct an equation of a line that goes through point #(8,-9)#. Examples are: #a=1, b=0, c=-8# Equation: #x-8=0# #a=2, b=0, c=16# Equation #2x-16=0# Obviously, all equations are equivalent to each other and can be reduced to a form #x=8#.

Sadie Allen · Answer

undefined The equation of the line with an undefined slope passing through point (8, -9) is x = 8.