How do you graph #x-y=1 #?

Graph:

#x-y=1#

X-intercept: value of #x# when #y=0#

Substitute #0# for #y# and solve for #x#.

x-0=1#

#x=1#

The x-intercept is #(1,0)#. Plot this point.

Y-intercept: value of #y# when #x=0#

Substitute #0# for #x# and solve for #y#.

#0-y=1#

#-y=1#

Multiply both sides by #-1#. This will reverse the signs.

#-1(-y)=1xx-1#

#y=-1#

The y-intercept is #(0,-1)#. Plot this point.

Draw a straight line through the points.

graph{x-y=1 [-10, 10, -5, 5]}

#" "#
We are given the equation: #color(red)(x-y=1#

How do we graph this linear equation ?

We have

#color(blue)(x-y=1#

The given equation can be reduced to a more simpler form.

Subtract #color(red)(x# from both sides of the equation:

#rArr x-y-x=1-x#

#rArr cancel x-y-cancel x=1-x#

#rArr -y = 1-x#

Multiply both sides of the equation by #color(red)((-1)#

#rArr -y*(-1) = (1-x)(-1)#

#rArr y=x-1#

Now, we have the equation in Slope-Intercept Form:

#color(blue)(y=mx+b)#, where

#color(red)(m# is the Slope and

#color(red)(b# is the y-intercept.

Hence,

Slope : #color(blue)(1#

y-intercept :#color(blue)((0,-1)#

The x-intercept is where the graph crosses the x-axis

Set #color(red)(y=0# to find the x-intercept:

#rArr x-1=0#

Add #color(red)(1# to both sides of the equation:

#rArr x-1+1=0+1#

#rArr x-cancel 1+cancel 1=0+1#

#rArr x=1#

Hence #color(red)((1,0)# is the x-intercept.

Plot the points x-intercept and intercept on the graph.

Join the two points to get the straight line.

This is the graph of the linear equation.

Hope you find this solution useful.