Because the #y# value for both points is #3# by definition this is a horizontal line.
Horizontal lines have the equation #y = a# where #a# is the same value for #y# for all values of #x# and the slope is #m = 0#. For this problem the equation is:
#y = 3#
The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#
Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.
Substituting gives:
#y = color(red)(0)x + color(blue)(3)#
The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#
Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
Substituting gives:
#color(red)(0)x + color(blue)(1)y = color(green)(3)#
The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.
Substituting gives:
#(y - color(red)(3)) = color(blue)(0)(x - color(red)(c))#
Where #c# is any value.
