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.
First, we can substitute the slope in the problem for #color(red)(m)# and substitute the values from the point in the problem for #x# and #y# and solve for #color(blue)(b)#:
#3 = (color(red)(1/2) xx 15) + color(blue)(b)#
#3 = color(red)(15/2) + color(blue)(b)#
#3 - 15/2 = color(red)(15/2) - 15/2 + color(blue)(b)#
#(2/2 xx 3) - 15/2 = 0 + color(blue)(b)#
#6/2 - 15/2 = color(blue)(b)#
#(6 - 15)/2 = color(blue)(b)#
#-9/2 = color(blue)(b)#
#color(blue)(b) = -9/2#
We can now substitute #-9/2# for #color(blue)(b)# and the slope from the problem for #color(red)(m)# in the original formula to write the equation:
#y = color(red)(1/2)x + color(blue)(-9/2)#
#y = color(red)(1/2)x - color(blue)(9/2)#
