Step 1: Write in slope-point form
#color(white)("XXX")#Step 1a: Determine the slope
#color(white)("XXX")color(green)m=(Deltay)/(Deltax)=(11-7)/(-3-5)=4/(-8)=color(green)(-1/2)#
#color(white)("XXX")#Step 1b: Use one of the given points to write in slope-point form:
#color(white)("XXX")y-7=-1/2(x-5)#
Step 2: Convert into slope-intercept form:
#color(white)("XXX")#Note the slope-intercept form is
#color(white)("XXXXXX")y=color(green)(m)x+color(blue)b#
#color(white)("XXX")#for a line with slope #color(green)(m)# and y-intercept #color(blue)(b)#
#color(white)("XXX")y=color(green)(-1/2)x+5/2+7#
#color(white)("XXX")y=color(green)(-1/2)x+color(blue)(19/2)#
Here is the graph of #y=-1/2x+19/2# with the given points for verification purposes:
