What is the slope and intercept for #x - y + 1 = 0# and how would you graph it?

1 Answer
Oct 3, 2015

Answer:

Slope: #1#
y-intercept: #1#
x-intercept: #(-1)#

Explanation:

The general slope-intercept form for a line is
#color(white)("XXX")y=mx+b#
#color(white)("XXXXX")#where #m# is the slope and #b# is the y-intercept

#x-y+1=0#
can be converted into slope-intercept form by
adding #y# to both sides and then exchanging the sides:
#color(white)("XXX")x+1=y#
#color(white)("XXX")y=(1)x+1#
#color(white)("XXXXX")#Note that I have inserted the implied coefficient of #1# for #x#

Based on the general form we can see that
#color(white)("XXX")#the slope is #m=1#
and
#color(white)("XXX")#the y-intercept is #b=1#

Assuming the x-intercept is also required,
we note that the x-intercept is the value of #x# when #y=0#
#color(white)("XXX")x-(0)+1=0color(white)("XX")rarrcolor(white)("XX")x=-1#

The x and y-intercepts give us the points
#color(white)("XXX")(-1,0)# and #(0,1)# respectively.
If we plot these two points on the Cartesian plane and draw a straight line through them, we will obtain the required graph

graph{(x-y+1)((sqrt(x^2+(y-1)^2))-0.1)((sqrt((x+1)^2+y^2))-0.1)=0 [-5.25, 5.85, -2.02, 3.527]}